problem
stringlengths 1.31k
38k
| answer
stringlengths 3
6.3k
|
|---|---|
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Green
Row 8: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Green
Row 9: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Brown Brown Green
Row 10: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 11: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 12: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 13: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 14: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 15: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 16: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 17: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 18: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 19: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 20: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 25: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 26: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Green Green
Row 8: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Green Green
Row 9: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Green Green
Row 10: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 11: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 12: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 13: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 14: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 15: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 16: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 17: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 18: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 19: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 20: Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 25: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 26: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 14: Brown Brown Brown Brown Red Red Red Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 15: Brown Brown Brown Brown Red Red Red Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 16: Brown Brown Brown Brown Red Red Red Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 17: Brown Brown Brown Brown Red Red Red Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 18: Brown Brown Brown Brown Red Red Red Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 19: Brown Brown Brown Brown Red Red Red Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 20: Brown Brown Brown Brown Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue
Row 21: Brown Brown Brown Brown Red Red Red Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 27: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 14: Brown Brown Brown Brown Brown Brown Red Red Red Blue Blue Blue Blue Blue Blue Blue
Row 15: Brown Brown Brown Brown Brown Brown Red Red Red Blue Blue Blue Blue Blue Blue Blue
Row 16: Brown Brown Brown Brown Brown Brown Red Red Red Blue Blue Blue Blue Blue Blue Blue
Row 17: Brown Brown Brown Brown Brown Brown Red Red Red Blue Blue Blue Blue Blue Blue Blue
Row 18: Brown Brown Brown Brown Brown Brown Red Red Red Blue Blue Blue Blue Blue Blue Blue
Row 19: Brown Brown Brown Brown Brown Brown Red Red Red Blue Blue Blue Blue Blue Blue Blue
Row 20: Brown Brown Brown Brown Brown Brown Red Red Red Blue Blue Blue Blue Blue Blue Blue
Row 21: Brown Brown Brown Brown Brown Brown Red Red Red Blue Blue Blue Blue Blue Blue Blue
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 27: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 3
Input:
Row 1: Orange Black Black Black Black Black Black Black Black Orange
Row 2: Orange Black Black Black Black Black Black Black Black Orange
Row 3: Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 15: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 16: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 17: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 18: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 19: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 20: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 21: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 22: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 23: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 26: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Black Black Black Black Black Black Black Black Orange
Row 13: Orange Black Black Black Black Black Black Black Black Orange
Row 14: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 15: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 16: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 17: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 18: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 19: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 20: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 21: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 22: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 23: Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 26: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Brown Purple Purple Purple Purple Purple Purple Green Green
Row 2: Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Purple Green Green Green Green
Row 3: Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Purple Purple Purple Green Green
Row 4: Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Purple Purple Purple Green Green Green
Row 5: Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Purple Purple Purple Purple Green Green
Row 6: Pink Pink Pink Pink Pink Pink Orange Orange Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Green Green Green
Output:
Row 1: Pink Orange Brown Purple Green
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Pink Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink
Row 6: Brown Pink Brown Pink Brown Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Brown Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Brown Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Green Green Pink Green Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Green Pink
Row 10: Pink Green Green Green Green Green Pink Pink Green Green Green Green Green Green Green Pink Green Pink Green Green Green Green Green Green Green Green Pink Green Green
Row 11: Green Green Green Green Green Green Green Pink Green Green Green Green Green Green Green Pink Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green
Row 15: Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Yellow Green Green Yellow
Row 16: Yellow Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Green Green Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Brown
Row 2: Pink
Row 3: Green
Row 4: Yellow
Example 3
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Gray Black
Row 4: Black Gray Black Black Gray Black Black Black Gray Gray Black
Row 5: Black Gray Gray Gray Gray Black Black Black Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Black
Row 2: Gray
Here is the input grid for the test example:
Input:
Row 1: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 2: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 3: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 4: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 5: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 6: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 7: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 8: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 9: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 10: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 11: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 12: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 13: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 14: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 15: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 16: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 17: Green Green Green Green Green Green Green Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 18: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 19: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 20: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Row 21: Green Green Green Green Green Green Green Green Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Orange Purple Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Orange Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Orange Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple Purple Purple Purple Green Green Green Green Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Red Red Green Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Orange Orange Orange Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Orange Brown Orange Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Orange Brown Orange Brown Purple Purple Purple Purple Purple Green Green Green Green Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Orange Orange Orange Brown Purple Purple Purple Green Green Red Red Red Red Green Green
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple Purple Green Green Red Green Green Red Green Green
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple Purple Green Green Red Red Red Red Green Green
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Green Green Purple Orange Orange Orange
Row 4: Orange Orange Red Red Red Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange
Row 5: Orange Orange Red Pink Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Black Black Purple Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Black Black Purple Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Purple Purple Green Green Green Green Purple Purple Orange
Row 3: Orange Orange Red Red Red Orange Orange Purple Purple Green Purple Purple Green Purple Purple Orange
Row 4: Orange Red Pink Pink Pink Red Orange Purple Purple Green Green Green Green Purple Purple Orange
Row 5: Orange Red Pink Red Pink Red Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange
Row 6: Orange Red Pink Pink Pink Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Purple Purple Black Black Black Black Purple Purple Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Purple Purple Black Purple Purple Black Purple Purple Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Purple Purple Black Purple Purple Black Purple Purple Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Purple Purple Black Black Black Black Purple Purple Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange
Example 3
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Red Red Red Red Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Red Black Black Red Orange Orange Orange Gray Purple Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Red Black Black Red Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Brown Brown Brown Orange Orange Orange Orange Orange Orange Brown Red Brown Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Brown Black Brown Orange Orange Orange Orange Orange Orange Brown Brown Brown Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange Gray Purple Purple Gray Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Purple Black Purple Orange Orange Orange Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Purple Black Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Brown Brown Brown Orange Orange Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Brown Purple Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Gray Purple Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Gray Purple Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange
Row 26: Orange Orange Orange Orange Orange Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 27: Orange Orange Orange Orange Orange Yellow Purple Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 28: Orange Orange Orange Orange Orange Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 29: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Red Red Red Red Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Red Red Black Black Black Black Red Red Gray Purple Purple Purple Gray Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Red Red Black Red Red Black Red Red Gray Purple Gray Purple Gray Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Red Red Black Red Red Black Red Red Gray Purple Purple Purple Gray Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Red Red Black Black Black Black Red Red Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Brown Brown Brown Orange Orange Orange Orange Orange Brown Red Red Red Brown Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Brown Black Black Black Brown Orange Orange Orange Orange Brown Red Brown Red Brown Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Brown Black Brown Black Brown Orange Orange Orange Orange Brown Red Red Red Brown Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Brown Black Black Black Brown Orange Orange Orange Orange Orange Brown Brown Brown Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Purple Purple Purple Orange Orange Gray Gray Purple Purple Purple Purple Gray Gray Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Purple Black Black Black Purple Orange Gray Gray Purple Gray Gray Purple Gray Gray Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Purple Black Purple Black Purple Orange Gray Gray Purple Purple Purple Purple Gray Gray Orange Orange Orange
Row 19: Orange Brown Brown Brown Orange Purple Black Purple Black Purple Orange Orange Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange
Row 20: Brown Purple Purple Purple Brown Purple Black Black Black Purple Orange Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange
Row 21: Brown Purple Brown Purple Brown Orange Purple Purple Purple Orange Orange Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange
Row 22: Brown Purple Purple Purple Brown Orange Purple Purple Purple Orange Orange Orange Orange Orange Purple Gray Gray Gray Purple Orange Orange Orange
Row 23: Orange Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Gray Purple Gray Purple Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Gray Purple Gray Purple Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Purple Gray Gray Gray Purple Orange Orange Orange
Row 26: Orange Orange Orange Orange Yellow Purple Purple Purple Yellow Orange Orange Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange
Row 27: Orange Orange Orange Orange Yellow Purple Yellow Purple Yellow Orange Orange Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange
Row 28: Orange Orange Orange Orange Yellow Purple Purple Purple Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 29: Orange Orange Orange Orange Orange Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Pink Purple Orange Orange Orange Orange
Row 4: Orange Orange Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange
Row 5: Orange Orange Purple Gray Gray Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Red Red Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Red Pink Orange
Row 10: Orange Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange
Row 11: Orange Purple Pink Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Purple Purple Purple Orange Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Pink Gray Orange Orange Gray Red Gray Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Gray Red Gray Orange Orange Orange Orange Orange Gray Purple Gray Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Red Red Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Red Gray Gray Red Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange Orange Red Purple Red Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Pink Red Pink Orange Orange Red Red Red Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Red Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 26: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 27: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Pink Pink Pink Purple Orange Orange Orange
Orange Orange Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Pink Purple Pink Purple Orange Orange Orange
Purple Purple Gray Gray Gray Gray Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Pink Pink Pink Purple Orange Orange Orange
Purple Purple Gray Purple Purple Gray Purple Purple Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange
Purple Purple Gray Gray Gray Gray Purple Purple Orange Orange Orange Orange Purple Purple Red Red Red Red Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Purple Purple Red Purple Purple Red Purple Purple Orange Orange Orange Orange Orange Pink Pink Pink Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Red Red Red Red Purple Purple Orange Orange Orange Orange Pink Red Red Red Pink
Orange Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Pink Red Pink Red Pink
Purple Pink Pink Pink Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Pink Red Red Red Pink
Purple Pink Purple Pink Purple Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange
Purple Pink Pink Pink Purple Orange Orange Orange Orange Gray Pink Pink Pink Gray Gray Red Red Red Gray Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange
Orange Purple Purple Purple Orange Orange Orange Orange Orange Gray Pink Gray Pink Gray Gray Red Gray Red Gray Orange Orange Orange Gray Purple Purple Purple Gray Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Pink Pink Pink Gray Gray Red Gray Red Gray Orange Orange Orange Gray Purple Gray Purple Gray Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Orange Gray Red Red Red Gray Orange Orange Orange Gray Purple Purple Purple Gray Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Red Red Orange Orange Orange Orange Orange
Orange Orange Red Red Gray Gray Gray Gray Red Red Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange Red Purple Purple Purple Red Orange Orange Orange Orange
Orange Orange Red Red Gray Red Red Gray Red Red Orange Orange Orange Orange Orange Pink Red Red Red Pink Red Purple Red Purple Red Orange Orange Orange Orange
Orange Orange Red Red Gray Gray Gray Gray Red Red Orange Orange Orange Orange Orange Pink Red Pink Red Pink Red Purple Purple Purple Red Orange Orange Orange Orange
Orange Orange Orange Orange Red Red Red Red Orange Orange Orange Pink Pink Pink Orange Pink Red Red Red Pink Orange Red Red Red Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Red Red Red Pink Orange Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Red Pink Red Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Red Red Red Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Purple Blue Blue Purple Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple Blue Blue Blue Blue
Row 2: Purple Blue Purple Blue Blue Purple Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple Blue Blue Blue
Row 3: Blue Purple Blue Purple Blue Blue Purple Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple Blue Blue
Row 4: Blue Blue Purple Blue Purple Blue Blue Purple Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple Blue
Row 5: Blue Blue Blue Purple Blue Purple Blue Blue Purple Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple
Row 6: Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple Blue Blue Blue Blue Purple Blue Purple Blue Blue
Row 7: Blue Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple Blue Blue Blue Blue Purple Blue Purple Blue
Row 8: Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple Blue Blue Blue Blue Purple Blue Purple
Row 9: Blue Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple Blue Blue Blue Blue Purple Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple Blue Blue Blue Blue Purple
Row 11: Purple Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple Blue Blue Blue Blue
Row 12: Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple Blue Blue Blue
Row 13: Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple Blue Blue
Row 14: Purple Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple Blue
Row 15: Blue Purple Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple
Row 16: Blue Blue Purple Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Blue
Row 17: Blue Blue Blue Purple Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue
Row 18: Purple Blue Blue Blue Purple Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Purple
Row 19: Blue Purple Blue Blue Blue Purple Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 20: Purple Blue Purple Blue Blue Blue Purple Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Purple
Row 21: Blue Purple Blue Purple Blue Blue Blue Purple Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Blue Blue Purple Blue Purple Blue Blue Blue Purple Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Purple Blue Blue Purple Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple Blue Blue Blue Blue
Row 2: Purple Blue Yellow Blue Blue Yellow Blue Blue Blue Blue Yellow Blue Yellow Blue Blue Yellow Blue Blue Blue
Row 3: Blue Yellow Blue Purple Blue Blue Purple Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple Blue Blue
Row 4: Blue Blue Purple Blue Yellow Blue Blue Yellow Blue Blue Blue Blue Yellow Blue Yellow Blue Blue Yellow Blue
Row 5: Blue Blue Blue Yellow Blue Purple Blue Blue Purple Blue Blue Blue Blue Purple Blue Purple Blue Blue Purple
Row 6: Blue Blue Blue Blue Purple Blue Yellow Blue Blue Yellow Blue Blue Blue Blue Yellow Blue Yellow Blue Blue
Row 7: Blue Blue Blue Blue Blue Yellow Blue Purple Blue Blue Purple Blue Blue Blue Blue Purple Blue Purple Blue
Row 8: Blue Blue Blue Blue Blue Blue Purple Blue Yellow Blue Blue Yellow Blue Blue Blue Blue Yellow Blue Yellow
Row 9: Blue Blue Blue Blue Blue Blue Blue Yellow Blue Purple Blue Blue Purple Blue Blue Blue Blue Purple Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Yellow Blue Blue Yellow Blue Blue Blue Blue Yellow
Row 11: Purple Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Purple Blue Blue Purple Blue Blue Blue Blue
Row 12: Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Yellow Blue Blue Yellow Blue Blue Blue
Row 13: Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Purple Blue Blue Purple Blue Blue
Row 14: Purple Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Yellow Blue Blue Yellow Blue
Row 15: Blue Yellow Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Purple Blue Blue Purple
Row 16: Blue Blue Purple Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Yellow Blue Blue
Row 17: Blue Blue Blue Yellow Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Purple Blue
Row 18: Purple Blue Blue Blue Purple Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Yellow
Row 19: Blue Yellow Blue Blue Blue Yellow Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Row 20: Purple Blue Purple Blue Blue Blue Purple Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Purple
Row 21: Blue Yellow Blue Yellow Blue Blue Blue Yellow Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Blue Blue Purple Blue Purple Blue Blue Blue Purple Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue
Example 2
Input:
Row 1: Orange Gray Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Gray Orange Orange Orange Orange Orange
Row 3: Gray Orange Orange Gray Orange Orange Orange Orange
Row 4: Orange Gray Orange Orange Gray Orange Orange Orange
Row 5: Orange Orange Gray Orange Orange Gray Orange Orange
Row 6: Gray Orange Orange Gray Orange Orange Gray Orange
Row 7: Orange Gray Orange Orange Gray Orange Orange Gray
Row 8: Orange Orange Gray Orange Orange Gray Orange Orange
Row 9: Orange Orange Orange Gray Orange Orange Gray Orange
Row 10: Orange Orange Orange Orange Gray Orange Orange Gray
Row 11: Orange Orange Orange Orange Orange Gray Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Gray Orange
Row 13: Gray Orange Orange Orange Orange Orange Orange Gray
Row 14: Orange Gray Orange Orange Orange Orange Orange Orange
Row 15: Gray Orange Gray Orange Orange Orange Orange Orange
Row 16: Orange Gray Orange Gray Orange Orange Orange Orange
Row 17: Orange Orange Gray Orange Gray Orange Orange Orange
Row 18: Gray Orange Orange Gray Orange Gray Orange Orange
Row 19: Orange Gray Orange Orange Gray Orange Gray Orange
Row 20: Gray Orange Gray Orange Orange Gray Orange Gray
Row 21: Orange Gray Orange Gray Orange Orange Gray Orange
Row 22: Gray Orange Gray Orange Gray Orange Orange Gray
Row 23: Orange Gray Orange Gray Orange Gray Orange Orange
Row 24: Gray Orange Gray Orange Gray Orange Gray Orange
Row 25: Orange Gray Orange Gray Orange Gray Orange Gray
Output:
Row 1: Orange Gray Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Yellow Orange Orange Orange Orange Orange
Row 3: Gray Orange Orange Gray Orange Orange Orange Orange
Row 4: Orange Yellow Orange Orange Yellow Orange Orange Orange
Row 5: Orange Orange Gray Orange Orange Gray Orange Orange
Row 6: Gray Orange Orange Yellow Orange Orange Yellow Orange
Row 7: Orange Yellow Orange Orange Gray Orange Orange Gray
Row 8: Orange Orange Gray Orange Orange Yellow Orange Orange
Row 9: Orange Orange Orange Yellow Orange Orange Gray Orange
Row 10: Orange Orange Orange Orange Gray Orange Orange Yellow
Row 11: Orange Orange Orange Orange Orange Yellow Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Gray Orange
Row 13: Gray Orange Orange Orange Orange Orange Orange Yellow
Row 14: Orange Yellow Orange Orange Orange Orange Orange Orange
Row 15: Gray Orange Gray Orange Orange Orange Orange Orange
Row 16: Orange Yellow Orange Yellow Orange Orange Orange Orange
Row 17: Orange Orange Gray Orange Gray Orange Orange Orange
Row 18: Gray Orange Orange Yellow Orange Yellow Orange Orange
Row 19: Orange Yellow Orange Orange Gray Orange Gray Orange
Row 20: Gray Orange Gray Orange Orange Yellow Orange Yellow
Row 21: Orange Yellow Orange Yellow Orange Orange Gray Orange
Row 22: Gray Orange Gray Orange Gray Orange Orange Yellow
Row 23: Orange Yellow Orange Yellow Orange Yellow Orange Orange
Row 24: Gray Orange Gray Orange Gray Orange Gray Orange
Row 25: Orange Yellow Orange Yellow Orange Yellow Orange Yellow
Example 3
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray
Row 4: Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray
Row 5: Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue
Row 6: Blue Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Blue Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Blue Gray Blue Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Blue Gray Blue Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray
Row 4: Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray
Row 5: Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue
Row 6: Blue Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Yellow Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Blue Gray Blue Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Yellow Gray Yellow Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black Black Black Black Black Black Black Orange Black Orange Black Orange
Row 2: Orange Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black Black Black Black Black Black Black Orange Black Orange Black
Row 3: Black Orange Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black Black Black Black Black Black Black Orange Black Orange
Row 4: Black Black Orange Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black Black Black Black Black Black Black Orange Black
Row 5: Black Black Black Orange Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black Black Black Black Black Black Black Orange
Row 6: Black Black Black Black Orange Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Orange Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Orange Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Orange Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Orange Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Orange Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black Black
Row 12: Orange Black Black Black Black Black Black Black Black Black Orange Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black
Row 13: Black Orange Black Black Black Black Black Black Black Black Black Orange Black Orange Black Orange Black Orange Black Black Orange Black Orange Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black Black Black Black Black Black Black Orange Black Orange Black Orange
Orange Black Yellow Black Yellow Black Yellow Black Black Yellow Black Yellow Black Black Black Black Black Black Black Black Yellow Black Yellow Black
Black Yellow Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black Black Black Black Black Black Black Orange Black Orange
Black Black Orange Black Yellow Black Yellow Black Yellow Black Black Yellow Black Yellow Black Black Black Black Black Black Black Black Yellow Black
Black Black Black Yellow Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black Black Black Black Black Black Black Orange
Black Black Black Black Orange Black Yellow Black Yellow Black Yellow Black Black Yellow Black Yellow Black Black Black Black Black Black Black Black
Black Black Black Black Black Yellow Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black Black Black Black Black Black
Black Black Black Black Black Black Orange Black Yellow Black Yellow Black Yellow Black Black Yellow Black Yellow Black Black Black Black Black Black
Black Black Black Black Black Black Black Yellow Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black Black Black Black
Black Black Black Black Black Black Black Black Orange Black Yellow Black Yellow Black Yellow Black Black Yellow Black Yellow Black Black Black Black
Black Black Black Black Black Black Black Black Black Yellow Black Orange Black Orange Black Orange Black Black Orange Black Orange Black Black Black
Orange Black Black Black Black Black Black Black Black Black Orange Black Yellow Black Yellow Black Yellow Black Black Yellow Black Yellow Black Black
Black Yellow Black Black Black Black Black Black Black Black Black Yellow Black Orange Black Orange Black Orange Black Black Orange Black Orange Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange Orange Orange Orange Orange Green Orange Orange Red Orange Red Gray Orange Gray Green Orange Gray Orange Orange Orange Orange Orange Green Orange Orange Orange Orange
Row 2: Green Orange Orange Red Orange Gray Orange Green Orange Green Green Red Gray Orange Green Orange Orange Orange Red Orange Gray Green Orange Orange Red Orange Orange Orange
Row 3: Orange Orange Orange Gray Orange Green Orange Green Red Orange Orange Orange Green Orange Orange Orange Orange Orange Green Green Green Gray Red Orange Orange Orange Orange Green
Row 4: Green Gray Orange Orange Green Orange Orange Gray Orange Green Orange Green Orange Orange Orange Red Orange Gray Orange Orange Green Gray Orange Orange Orange Orange Red Green
Row 5: Orange Orange Orange Gray Orange Green Orange Red Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Gray Orange Gray Orange
Row 6: Orange Orange Orange Orange Green Orange Green Red Orange Orange Red Green Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Gray Red Orange Green Green Green Orange Orange Orange Orange Orange Red Orange Red Orange Gray Orange Red Orange Red Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Green Gray Orange Orange Gray Red Green Orange Green Orange
Row 9: Orange Orange Orange Red Orange Orange Orange Green Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Red Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Red Gray Orange Gray Green Orange Gray Orange Orange Orange Orange Orange Green Orange Orange Orange Orange
Row 2: Green Orange Orange Red Orange Gray Orange Green Orange Purple Purple Orange Gray Orange Green Orange Orange Orange Orange Orange Gray Green Orange Orange Red Orange Orange Orange
Row 3: Orange Orange Orange Gray Orange Green Orange Purple Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Purple Green Green Gray Red Orange Orange Orange Orange Green
Row 4: Green Gray Orange Orange Green Orange Orange Gray Orange Green Orange Green Orange Orange Orange Red Orange Gray Orange Orange Green Gray Orange Orange Orange Orange Orange Purple
Row 5: Orange Orange Orange Gray Orange Green Orange Red Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Gray Orange Gray Orange
Row 6: Orange Orange Orange Orange Green Orange Purple Orange Orange Orange Orange Purple Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Gray Red Orange Green Purple Green Orange Orange Orange Orange Orange Red Orange Red Orange Gray Orange Red Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Green Gray Orange Orange Gray Orange Purple Orange Green Orange
Row 9: Orange Orange Orange Red Orange Orange Orange Green Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Red Orange Orange Orange Orange
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Green Gray Blue Blue Gray Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Gray Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Purple Gray Blue Blue Gray Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Gray Blue Blue Blue Blue
Example 3
Input:
Row 1: Orange Gray Gray Orange Orange Green Red Orange Orange Orange
Row 2: Gray Orange Orange Green Orange Orange Orange Orange Green Orange
Row 3: Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange
Output:
Row 1: Orange Gray Gray Orange Orange Purple Orange Orange Orange Orange
Row 2: Gray Orange Orange Green Orange Orange Orange Orange Green Orange
Row 3: Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Red Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Gray Orange Orange
Row 5: Orange Orange Orange Orange Gray Brown
Row 6: Orange Orange Orange Orange Blue Black
Row 7: Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange
Output:
Row 1: Gray Orange Orange Orange Orange Orange
Row 2: Orange Gray Orange Orange Orange Orange
Row 3: Orange Orange Gray Orange Orange Orange
Row 4: Orange Orange Orange Gray Orange Orange
Row 5: Orange Orange Orange Orange Gray Brown
Row 6: Orange Orange Orange Orange Blue Black
Row 7: Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Yellow Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Green Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Yellow Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Green Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Example 3
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Blue Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Pink Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Blue Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Pink Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Black Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Blue Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 27: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 28: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 29: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 30: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Black Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Blue Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Purple Purple Purple Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Purple Brown Purple Purple Purple Purple Purple Brown Purple Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Blue Purple Purple Purple Purple Brown Purple Brown Brown Purple Purple Purple Purple Brown Purple Purple Brown Brown Brown Brown Brown
Row 9: Brown Purple Purple Purple Purple Purple Purple Brown Purple Brown Brown Purple Purple Brown Purple Brown Brown Brown Brown Brown Brown
Row 10: Brown Purple Purple Purple Purple Purple Purple Purple Brown Purple Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Brown
Row 11: Brown Purple Purple Purple Purple Purple Purple Brown Purple Brown Brown Brown Purple Brown Brown Purple Purple Brown Brown Brown Brown
Row 12: Brown Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Brown Purple Brown Purple Brown Brown Brown Brown Brown Brown
Row 13: Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Purple Purple Purple Purple Purple Purple Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Purple Brown Purple Purple Brown Brown Purple Purple Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Brown Purple Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Purple Purple Purple Purple Brown Purple Purple Brown Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Purple Purple Purple Purple Purple Brown Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Blue Blue Blue Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Blue Brown Blue Blue Blue Blue Blue Brown Blue Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Blue Blue Blue Blue Brown Blue Brown Brown Blue Blue Blue Blue Brown Blue Blue Brown Brown Brown Brown Brown
Row 9: Brown Blue Blue Blue Blue Blue Blue Brown Blue Brown Brown Blue Blue Brown Blue Brown Brown Brown Brown Brown Brown
Row 10: Brown Blue Blue Blue Blue Blue Blue Blue Brown Blue Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown Brown
Row 11: Brown Blue Blue Blue Blue Blue Blue Brown Blue Brown Brown Brown Blue Brown Brown Blue Blue Brown Brown Brown Brown
Row 12: Brown Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Brown Blue Brown Blue Brown Brown Brown Brown Brown Brown
Row 13: Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Blue Blue Blue Blue Blue Blue Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Blue Brown Blue Blue Brown Brown Blue Blue Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Brown Blue Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Blue Blue Blue Blue Brown Blue Blue Brown Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Blue Blue Blue Blue Blue Brown Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 2
Input:
Row 1: Black Black Black Black Black Black Black
Row 2: Black Pink Pink Pink Pink Pink Black
Row 3: Black Pink Pink Pink Black Pink Blue
Row 4: Black Pink Pink Black Black Black Black
Row 5: Black Black Pink Pink Black Black Black
Row 6: Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black
Row 2: Black Blue Blue Blue Blue Blue Black
Row 3: Black Blue Blue Blue Black Blue Black
Row 4: Black Blue Blue Black Black Black Black
Row 5: Black Black Blue Blue Black Black Black
Row 6: Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Green Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Red
Row 2: Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple
Row 6: Purple Blue Blue Purple Purple
Row 7: Purple Blue Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple
Purple Red Red Purple Purple
Purple Red Purple Purple Purple
Purple Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Green Pink Green Pink Green Pink Green Pink Green Pink Green Pink
Row 2: Orange Blue Orange Blue Orange Blue Orange Blue Orange Blue Orange Blue
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Gray Orange Gray Orange Gray Orange Gray Orange Gray Orange Gray Orange
Row 5: Yellow Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Pink Blue Pink Blue Pink Blue Pink Blue Pink Blue Pink Blue
Row 8: Green Orange Green Orange Green Orange Green Orange Green Orange Green Orange
Row 9: Orange Gray Orange Gray Orange Gray Orange Gray Orange Gray Orange Gray
Row 10: Green Blue Green Blue Green Blue Green Blue Green Blue Green Blue
Row 11: Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow
Row 12: Green Orange Green Orange Green Orange Green Orange Green Orange Green Orange
Row 13: Orange Green Orange Green Orange Green Orange Green Orange Green Orange Green
Row 14: Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green
Row 15: Blue Green Blue Green Blue Green Blue Green Blue Green Blue Green
Row 16: Gray Orange Gray Orange Gray Orange Gray Orange Gray Orange Gray Orange
Row 17: Orange Green Orange Green Orange Green Orange Green Orange Green Orange Green
Row 18: Blue Pink Blue Pink Blue Pink Blue Pink Blue Pink Blue Pink
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Yellow
Row 21: Orange Gray Orange Gray Orange Gray Orange Gray Orange Gray Orange Gray
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Blue Orange Blue Orange Blue Orange Blue Orange Blue Orange Blue Orange
Row 24: Pink Green Pink Green Pink Green Pink Green Pink Green Pink Green
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green
Row 3: Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow
Row 4: Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green
Row 5: Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow
Row 6: Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue
Row 11: Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow
Row 14: Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue
Row 19: Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green
Row 20: Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow
Row 21: Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green
Row 22: Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Example 3
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Orange Black Orange Black Orange Black Orange Black Orange Black Orange Black Orange Black Orange Black
Row 2: Black Green Black Green Black Green Black Green Black Green Black Green Black Green Black Green
Row 3: Green Black Green Black Green Black Green Black Green Black Green Black Green Black Green Black
Row 4: Black Orange Black Orange Black Orange Black Orange Black Orange Black Orange Black Orange Black Orange
Here is the input grid for the test example:
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Purple Green Purple Green Purple Green Purple Green Purple Green Purple Green Purple Green
Purple Brown Purple Brown Purple Brown Purple Brown Purple Brown Purple Brown Purple Brown Purple
Pink Blue Pink Blue Pink Blue Pink Blue Pink Blue Pink Blue Pink Blue Pink
Purple Brown Purple Brown Purple Brown Purple Brown Purple Brown Purple Brown Purple Brown Purple
Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue
Red Pink Red Pink Red Pink Red Pink Red Pink Red Pink Red Pink Red
Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown
Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red
Blue Black Blue Black Blue Black Blue Black Blue Black Blue Black Blue Black Blue
Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red
Green Brown Green Brown Green Brown Green Brown Green Brown Green Brown Green Brown Green
Blue Red Blue Red Blue Red Blue Red Blue Red Blue Red Blue Red Blue
Red Blue Red Blue Red Blue Red Blue Red Blue Red Blue Red Blue Red
Brown Green Brown Green Brown Green Brown Green Brown Green Brown Green Brown Green Brown
Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black
Black Blue Black Blue Black Blue Black Blue Black Blue Black Blue Black Blue Black
Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black
Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue
Pink Red Pink Red Pink Red Pink Red Pink Red Pink Red Pink Red Pink
Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown
Brown Purple Brown Purple Brown Purple Brown Purple Brown Purple Brown Purple Brown Purple Brown
Blue Pink Blue Pink Blue Pink Blue Pink Blue Pink Blue Pink Blue Pink Blue
Brown Purple Brown Purple Brown Purple Brown Purple Brown Purple Brown Purple Brown Purple Brown
Purple Green Purple Green Purple Green Purple Green Purple Green Purple Green Purple Green Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Purple Pink Yellow
Row 2: Purple Purple Green Purple
Row 3: Yellow Purple Purple Purple
Row 4: Yellow Purple Purple Green
Output:
Row 1: Black Black Black Black Pink Purple Pink Yellow Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Purple Purple Green Purple Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Yellow Purple Purple Purple Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Yellow Purple Purple Green Black Black Black Black Black Black Black Black
Row 5: Pink Purple Pink Yellow Pink Purple Pink Yellow Black Black Black Black Pink Purple Pink Yellow
Row 6: Purple Purple Green Purple Purple Purple Green Purple Black Black Black Black Purple Purple Green Purple
Row 7: Yellow Purple Purple Purple Yellow Purple Purple Purple Black Black Black Black Yellow Purple Purple Purple
Row 8: Yellow Purple Purple Green Yellow Purple Purple Green Black Black Black Black Yellow Purple Purple Green
Row 9: Black Black Black Black Pink Purple Pink Yellow Pink Purple Pink Yellow Pink Purple Pink Yellow
Row 10: Black Black Black Black Purple Purple Green Purple Purple Purple Green Purple Purple Purple Green Purple
Row 11: Black Black Black Black Yellow Purple Purple Purple Yellow Purple Purple Purple Yellow Purple Purple Purple
Row 12: Black Black Black Black Yellow Purple Purple Green Yellow Purple Purple Green Yellow Purple Purple Green
Row 13: Black Black Black Black Pink Purple Pink Yellow Pink Purple Pink Yellow Black Black Black Black
Row 14: Black Black Black Black Purple Purple Green Purple Purple Purple Green Purple Black Black Black Black
Row 15: Black Black Black Black Yellow Purple Purple Purple Yellow Purple Purple Purple Black Black Black Black
Row 16: Black Black Black Black Yellow Purple Purple Green Yellow Purple Purple Green Black Black Black Black
Example 2
Input:
Row 1: Brown Brown
Row 2: Pink Brown
Row 3: Pink Brown
Output:
Row 1: Brown Brown Brown Brown
Row 2: Pink Brown Pink Brown
Row 3: Pink Brown Pink Brown
Row 4: Black Black Brown Brown
Row 5: Black Black Pink Brown
Row 6: Black Black Pink Brown
Row 7: Black Black Brown Brown
Row 8: Black Black Pink Brown
Row 9: Black Black Pink Brown
Example 3
Input:
Row 1: Blue Blue Blue Gray
Row 2: Green Red Blue Blue
Row 3: Blue Pink Orange Blue
Output:
Row 1: Blue Blue Blue Gray Blue Blue Blue Gray Blue Blue Blue Gray Black Black Black Black
Row 2: Green Red Blue Blue Green Red Blue Blue Green Red Blue Blue Black Black Black Black
Row 3: Blue Pink Orange Blue Blue Pink Orange Blue Blue Pink Orange Blue Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Blue Blue Blue Gray Blue Blue Blue Gray
Row 5: Black Black Black Black Black Black Black Black Green Red Blue Blue Green Red Blue Blue
Row 6: Black Black Black Black Black Black Black Black Blue Pink Orange Blue Blue Pink Orange Blue
Row 7: Blue Blue Blue Gray Black Black Black Black Black Black Black Black Blue Blue Blue Gray
Row 8: Green Red Blue Blue Black Black Black Black Black Black Black Black Green Red Blue Blue
Row 9: Blue Pink Orange Blue Black Black Black Black Black Black Black Black Blue Pink Orange Blue
Here is the input grid for the test example:
Input:
Row 1: Red Orange Red Red
Row 2: Gray Red Red Orange
Row 3: Red Orange Red Gray
Row 4: Red Gray Red Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Orange Red Red Black Black Black Black Red Orange Red Red Red Orange Red Red
Gray Red Red Orange Black Black Black Black Gray Red Red Orange Gray Red Red Orange
Red Orange Red Gray Black Black Black Black Red Orange Red Gray Red Orange Red Gray
Red Gray Red Orange Black Black Black Black Red Gray Red Orange Red Gray Red Orange
Black Black Black Black Red Orange Red Red Red Orange Red Red Black Black Black Black
Black Black Black Black Gray Red Red Orange Gray Red Red Orange Black Black Black Black
Black Black Black Black Red Orange Red Gray Red Orange Red Gray Black Black Black Black
Black Black Black Black Red Gray Red Orange Red Gray Red Orange Black Black Black Black
Red Orange Red Red Black Black Black Black Red Orange Red Red Black Black Black Black
Gray Red Red Orange Black Black Black Black Gray Red Red Orange Black Black Black Black
Red Orange Red Gray Black Black Black Black Red Orange Red Gray Black Black Black Black
Red Gray Red Orange Black Black Black Black Red Gray Red Orange Black Black Black Black
Red Orange Red Red Black Black Black Black Red Orange Red Red Black Black Black Black
Gray Red Red Orange Black Black Black Black Gray Red Red Orange Black Black Black Black
Red Orange Red Gray Black Black Black Black Red Orange Red Gray Black Black Black Black
Red Gray Red Orange Black Black Black Black Red Gray Red Orange Black Black Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Black Green Red Red Red Red Blue Red Red Green Green Green Green Red Red
Row 2: Green Red Green Red Red Red Red Red Red Red Green Red Black Green Red Red
Row 3: Green Green Green Red Red Red Red Red Red Red Green Black Black Green Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Green Green Green Green Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Red
Row 7: Red Red Blue Red Red Red Red Red Red Blue Blue Red Red Red Red Red
Row 8: Red Blue Blue Red Red Red Red Red Red Red Red Red Red Red Green Green
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Red
Row 11: Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Green Black
Row 12: Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Green Green
Row 13: Red Red Red Red Red Red Blue Red Red Blue Red Red Red Red Red Red
Output:
Row 1: Green Black Green Red Red Red Red Blue Red Red Green Green Green Green Red Red
Row 2: Green Red Green Red Red Red Red Red Red Red Green Red Black Green Red Red
Row 3: Green Green Green Red Red Red Red Red Red Red Green Black Black Green Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Green Green Green Green Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Black Red Red Red Red Red
Row 7: Red Red Black Red Red Red Red Red Red Black Black Red Red Red Red Red
Row 8: Red Black Black Red Red Red Red Red Red Red Red Red Red Red Green Green
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Red
Row 11: Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Green Black
Row 12: Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Green Green
Row 13: Red Red Red Red Red Red Blue Red Red Blue Red Red Red Red Red Red
Example 2
Input:
Row 1: Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray Gray Gray Brown Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Orange Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Brown Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Brown Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Brown Gray Gray Gray Gray Brown Brown Brown
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray Gray Gray Orange Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Orange Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Orange Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Orange Gray Gray Gray Gray Brown Brown Brown
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Example 3
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Blue Blue Blue Blue Orange Orange Orange Orange Orange Yellow Yellow Yellow Orange
Row 5: Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Yellow Purple Yellow Orange
Row 6: Blue Orange Orange Orange Blue Blue Blue Orange Orange Orange Orange Orange Yellow Yellow Yellow Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Blue Blue Orange Orange Orange Yellow Yellow Yellow Yellow Orange Orange Orange Blue Orange
Row 22: Orange Orange Blue Blue Blue Orange Orange Yellow Purple Purple Yellow Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Orange Yellow Purple Purple Yellow Orange Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Yellow Purple Purple Yellow Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Blue Blue Blue Blue Orange Orange Orange Orange Orange Yellow Yellow Yellow Orange
Row 5: Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Yellow Purple Yellow Orange
Row 6: Blue Orange Orange Orange Blue Blue Blue Orange Orange Orange Orange Orange Yellow Yellow Yellow Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Blue Blue Orange Orange Orange Yellow Yellow Yellow Yellow Orange Orange Orange Purple Orange
Row 22: Orange Orange Blue Blue Blue Orange Orange Yellow Purple Purple Yellow Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Orange Yellow Purple Purple Yellow Orange Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Yellow Purple Purple Yellow Orange Orange Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Black Gray Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Black Gray Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Brown Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Black Gray Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Black Gray Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Brown Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow
Row 2: Yellow Yellow
Row 3: Yellow Yellow
Row 4: Yellow Yellow
Row 5: Yellow Yellow
Row 6: Yellow Yellow
Row 7: Yellow Yellow
Row 8: Yellow Yellow
Row 9: Yellow Yellow
Row 10: Yellow Green
Row 11: Yellow Green
Row 12: Yellow Green
Row 13: Yellow Green
Row 14: Yellow Green
Row 15: Yellow Yellow
Row 16: Yellow Yellow
Row 17: Yellow Yellow
Row 18: Yellow Yellow
Row 19: Yellow Yellow
Row 20: Yellow Yellow
Output:
Row 1: Green Green
Row 2: Green Green
Row 3: Green Green
Row 4: Green Green
Row 5: Green Green
Row 6: Green Green
Row 7: Green Green
Row 8: Green Green
Row 9: Green Green
Row 10: Green Green
Example 2
Input:
Row 1: Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red
Row 4: Orange Red Red Red Red Red Red Red Red
Row 5: Red Orange Red Red Red Red Red Red Red
Row 6: Red Red Orange Red Red Red Red Red Red
Row 7: Red Red Orange Red Red Red Red Red Red
Row 8: Orange Orange Orange Orange Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red
Output:
Row 1: Orange Orange Red Red Red Red Red Red
Row 2: Orange Orange Red Red Red Red Red Red
Row 3: Red Red Orange Orange Red Red Red Red
Row 4: Red Red Orange Orange Red Red Red Red
Row 5: Red Red Red Red Orange Orange Red Red
Row 6: Red Red Red Red Orange Orange Red Red
Row 7: Red Red Red Red Orange Orange Red Red
Row 8: Red Red Red Red Orange Orange Red Red
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black
Row 13: Yellow Yellow Black Black Black Black Black Black Black Black Black
Row 14: Black Yellow Black Yellow Black Black Black Black Black Black Black
Row 15: Yellow Yellow Yellow Black Yellow Black Black Black Black Black Black
Row 16: Black Black Yellow Black Black Black Black Black Black Black Black
Row 17: Black Black Black Yellow Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black
Row 24: Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Yellow Yellow Yellow Yellow Black Black Black Black Black Black
Row 2: Yellow Yellow Yellow Yellow Black Black Black Black Black Black
Row 3: Black Black Yellow Yellow Black Black Yellow Yellow Black Black
Row 4: Black Black Yellow Yellow Black Black Yellow Yellow Black Black
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Black Black Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Black Black Yellow Yellow
Row 7: Black Black Black Black Yellow Yellow Black Black Black Black
Row 8: Black Black Black Black Yellow Yellow Black Black Black Black
Row 9: Black Black Black Black Black Black Yellow Yellow Black Black
Row 10: Black Black Black Black Black Black Yellow Yellow Black Black
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Red Red Red Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Red Red Gray Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Gray Gray Gray Red Red Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Red Red Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Red Red Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Red Red Gray Gray Gray Gray Gray Gray
Gray Gray Red Red Red Red Gray Gray Gray Gray Gray Gray
Gray Gray Red Red Red Red Gray Gray Gray Gray Gray Gray
Gray Gray Red Red Red Red Red Red Gray Gray Red Red
Gray Gray Red Red Red Red Red Red Gray Gray Red Red
Gray Gray Red Red Red Red Gray Gray Red Red Red Red
Gray Gray Red Red Red Red Gray Gray Red Red Red Red
Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Pink Pink Pink Pink Green Green Pink Green Pink Green Green Pink Pink Pink Pink Pink Green Pink
Row 2: Green Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green
Row 3: Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Pink Pink Green
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Pink Yellow Yellow Yellow Yellow Pink Pink Green
Row 5: Pink Pink Green Green Pink Pink Pink Pink Pink Green Green Pink Yellow Yellow Yellow Yellow Pink Pink Pink
Row 6: Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Green Pink Pink Pink Green Pink Green Pink Pink Pink Pink Pink Pink Green Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Green Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Green Pink Pink
Row 11: Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Green Pink Pink Pink
Row 12: Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Green Pink Green Pink Pink Pink Pink Pink Pink
Row 13: Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Green
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Green Green Pink Pink Green Pink Pink
Row 15: Pink Pink Pink Pink Pink Green Pink Pink Green Pink Green Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink
Row 18: Green Pink Pink Green Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Green Pink Pink Pink
Row 20: Green Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Green Pink Green Pink Pink Pink Pink Pink Green Pink Pink Green Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Green Green Pink Green Pink Green Green Pink Pink Pink Pink Pink Green Pink
Row 2: Green Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green
Row 3: Pink Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Green Green Green
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Yellow Yellow Yellow Yellow Green Green Green
Row 5: Pink Pink Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Pink Pink Pink
Row 6: Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Pink Pink Pink
Row 7: Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Green Green Green Green Pink Pink Pink
Row 8: Pink Pink Pink Pink Green Pink Pink Pink Green Pink Green Pink Green Green Green Green Pink Green Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Green Green Green Green Green Pink Pink
Row 11: Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Green Green Green Green Pink Pink Pink
Row 12: Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Green Pink Green Green Green Green Pink Pink Pink
Row 13: Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Pink Pink Green
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Green Green Green Green Green Pink Pink
Row 15: Pink Pink Pink Pink Pink Green Pink Pink Green Pink Green Pink Green Green Green Green Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Pink Pink Pink
Row 17: Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Green Green Green Pink Pink
Row 18: Green Pink Pink Green Pink Pink Green Pink Pink Pink Green Pink Pink Pink Green Green Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Green Pink Pink Pink
Row 20: Green Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Green Pink Green Pink Pink Pink Pink Pink Green Pink Pink Green Pink Pink Pink Pink Pink Pink Pink
Example 2
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Gray Green Green Green Green Gray Green Green Green Gray Gray Green Gray
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Orange Orange Orange Green Green Green Green Green
Row 5: Gray Green Green Green Green Orange Orange Orange Green Green Green Green Green
Row 6: Green Green Green Green Green Orange Orange Orange Green Green Green Green Green
Row 7: Green Green Green Green Green Orange Orange Orange Green Green Green Green Green
Row 8: Green Green Green Green Green Orange Orange Orange Green Green Green Green Green
Row 9: Green Green Green Gray Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Gray
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Gray Green Green Green Green Gray Green Green Green Gray Gray Green Gray
Row 3: Green Green Green Green Green Gray Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Orange Orange Orange Green Green Green Green Green
Row 5: Gray Gray Gray Gray Gray Orange Orange Orange Green Green Green Green Green
Row 6: Green Green Green Green Green Orange Orange Orange Green Green Green Green Green
Row 7: Green Green Green Green Green Orange Orange Orange Green Green Green Green Green
Row 8: Green Green Green Green Green Orange Orange Orange Green Green Green Green Green
Row 9: Green Green Green Gray Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Gray
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Black Pink Pink Pink Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Black Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink
Row 5: Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Black Black Pink Pink Pink Pink
Row 8: Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Black Pink Black Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink
Row 21: Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 24: Black Pink Pink Black Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Black Black Pink Pink Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Black Pink Black Pink Pink Pink Pink Black Pink Pink Pink Pink Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Black Pink Pink Pink Pink Black Pink Pink Pink Pink Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink
Row 5: Pink Pink Pink Black Pink Pink Pink Pink Black Pink Pink Pink Pink Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink
Row 6: Pink Pink Pink Black Pink Pink Pink Pink Black Pink Pink Pink Pink Black Black Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black Black Black Pink Pink Pink Pink
Row 8: Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black Black Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Black Black Black Black Black Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Black Black Black Black Black Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Black Black Black Black Black Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Black Black Pink Black Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Black Black Black Black Black Pink Pink Pink Pink Pink Black Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Black Pink Black Black Black Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink
Row 19: Pink Pink Pink Black Pink Black Black Black Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Black Pink Black Pink Black Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink
Row 21: Pink Pink Pink Black Pink Black Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Black Pink Black Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Black Pink Black Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 24: Black Pink Pink Black Pink Black Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink
Here is the input grid for the test example:
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Orange
Row 5: Black Black Black Black Black Black Black Black Orange Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Orange Black Black
Row 7: Orange Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black
Row 8: Black Black Black Black Orange Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black
Row 9: Orange Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black
Row 12: Black Black Black Black Black Orange Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black Black
Row 13: Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Orange Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Orange Black Black Black Orange Orange Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Orange Black Black Black Black Black Black Black Orange
Row 16: Black Black Orange Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Orange Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Orange Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Orange Black Black Black Black Orange Black Black Black Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange
Black Black Black Black Black Black Black Black Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Black Black
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black
Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black
Black Black Black Black Black Orange Black Black Orange Black Black Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Black Orange Black Black
Black Black Black Black Black Black Black Black Orange Black Black Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Black Black Black Black
Orange Black Black Black Orange Black Black Black Black Black Black Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Black Black Orange Orange Orange Black Orange Black Black Black Orange
Black Black Orange Black Black Orange Black Black Black Black Black Black Orange Orange Orange Black Black Orange Orange Orange Black Orange Black Black Black Black
Black Black Black Black Black Black Orange Black Black Black Black Black Orange Orange Orange Black Black Black Orange Orange Black Orange Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Orange Black Orange Black Black Black Orange Orange Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Orange Black Orange Black Black Black Black Orange Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Orange Black Black Black Black Orange Black Black Black Black Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Green Red
Row 2: Green Green Red
Row 3: Red Red Yellow
Row 4: Red Green Pink
Row 5: Green Blue Yellow
Row 6: Pink Yellow Brown
Row 7: Purple Blue Brown
Row 8: Black Red Gray
Row 9: Brown Gray Gray
Row 10: Pink Green Brown
Row 11: Green Yellow Purple
Row 12: Brown Purple Brown
Row 13: Pink Pink Red
Row 14: Pink Red Gray
Row 15: Red Gray Purple
Row 16: Green Purple Green
Row 17: Purple Pink Purple
Row 18: Green Purple Pink
Row 19: Yellow Red Gray
Row 20: Red Orange Gray
Row 21: Gray Gray Brown
Output:
Row 1: Purple Blue Brown
Row 2: Black Red Gray
Row 3: Brown Gray Gray
Example 2
Input:
Row 1: Gray Blue Pink Gray Red Purple Gray Yellow Purple Pink Blue Pink Pink Pink Brown
Row 2: Blue Gray Red Red Green Red Yellow Gray Yellow Blue Yellow Orange Pink Pink Red
Row 3: Pink Red Blue Green Blue Red Purple Yellow Yellow Pink Orange Pink Brown Red Red
Output:
Row 1: Gray Red Purple
Row 2: Red Green Red
Row 3: Green Blue Red
Example 3
Input:
Row 1: Purple Black Yellow Yellow Red Black Orange Yellow Green Brown Red Brown Gray Yellow Blue Green Blue Blue Green Blue Green
Row 2: Black Purple Gray Red Yellow Gray Yellow Green Pink Red Gray Blue Yellow Green Purple Blue Purple Gray Blue Blue Red
Row 3: Yellow Gray Gray Black Gray Brown Green Pink Green Blue Blue Green Blue Purple Brown Blue Gray Gray Green Red Pink
Output:
Row 1: Brown Red Brown
Row 2: Red Gray Blue
Row 3: Blue Blue Green
Here is the input grid for the test example:
Input:
Row 1: Black Black Red Orange
Row 2: Black Purple Brown Orange
Row 3: Red Brown Blue Pink
Row 4: Orange Orange Pink Purple
Row 5: Brown Blue Green Blue
Row 6: Blue Purple Purple Orange
Row 7: Green Purple Brown Black
Row 8: Blue Orange Black Yellow
Row 9: Blue Gray Green Pink
Row 10: Gray Brown Pink Pink
Row 11: Green Pink Red Brown
Row 12: Yellow Red Brown Red
Row 13: Gray Gray Green Orange
Row 14: Gray Blue Orange Brown
Row 15: Green Orange Yellow Gray
Row 16: Orange Brown Gray Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Gray Green Pink
Gray Brown Pink Pink
Green Pink Red Brown
Yellow Red Brown Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black Black Black Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple
Row 4: Purple Orange Orange Orange Orange Yellow Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple
Row 5: Purple Orange Purple Purple Orange Yellow Purple Purple Purple Yellow Purple Purple Purple Purple Purple Brown Brown Brown Brown Purple Black Purple Purple Purple Purple Black Purple Purple Purple
Row 6: Purple Orange Purple Purple Orange Yellow Yellow Yellow Yellow Yellow Purple Purple Gray Gray Gray Brown Purple Purple Brown Purple Black Purple Purple Purple Purple Black Purple Purple Purple
Row 7: Purple Orange Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Gray Purple Gray Brown Purple Purple Brown Purple Black Black Black Black Black Black Purple Purple Purple
Row 8: Purple Orange Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Gray Purple Gray Brown Purple Purple Brown Red Red Red Red Purple Blue Blue Blue Blue Purple
Row 9: Purple Orange Orange Orange Orange Purple Purple Purple Green Green Green Purple Gray Purple Gray Brown Brown Brown Brown Red Purple Purple Red Purple Blue Purple Purple Blue Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Green Purple Gray Gray Gray Purple Purple Purple Purple Red Red Red Red Purple Blue Purple Purple Blue Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Blue Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Blue Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Blue Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Blue Blue Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Black Black
Row 2: Black Black
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Pink Pink Pink
Row 5: Pink Pink Pink Pink Black Black Black Pink Pink Pink Purple Purple Purple Purple Purple Orange Pink Pink Pink Orange Pink Pink Pink
Row 6: Pink Pink Pink Pink Black Pink Black Pink Pink Pink Purple Pink Pink Pink Purple Orange Pink Pink Pink Orange Pink Pink Pink
Row 7: Pink Pink Pink Pink Black Pink Black Pink Pink Pink Purple Pink Pink Pink Purple Orange Pink Pink Pink Orange Pink Pink Pink
Row 8: Pink Pink Pink Pink Black Pink Black Pink Pink Pink Purple Pink Pink Pink Purple Orange Pink Pink Pink Orange Pink Pink Pink
Row 9: Pink Pink Pink Pink Black Pink Black Pink Pink Pink Purple Pink Pink Pink Purple Orange Pink Pink Pink Orange Pink Pink Pink
Row 10: Pink Pink Pink Pink Black Pink Black Pink Pink Pink Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Pink Pink Pink
Row 11: Pink Pink Pink Pink Black Black Black Pink Pink Pink Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Red Red Red Pink Gray Gray Gray Pink Pink Green Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Red Pink Red Pink Gray Pink Gray Pink Pink Green Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Red Pink Red Pink Gray Pink Gray Pink Pink Green Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Red Red Red Pink Gray Gray Gray Pink Pink Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Orange Orange
Row 2: Orange Orange
Example 3
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Orange Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Gray
Row 4: Orange Gray Orange Gray Pink Pink Pink Pink Pink Pink Gray Gray Brown Gray Brown Gray
Row 5: Orange Gray Orange Gray Pink Gray Gray Gray Gray Pink Gray Gray Brown Brown Brown Gray
Row 6: Orange Gray Orange Gray Pink Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray
Row 7: Orange Gray Orange Gray Pink Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray
Row 8: Orange Orange Orange Gray Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Black Black Black Black Gray Gray Gray Red Red Red Red Red Gray Gray Gray
Row 11: Gray Black Gray Gray Black Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray
Row 12: Gray Black Black Black Black Gray Gray Gray Red Red Red Red Red Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Pink Pink
Row 2: Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Green Green Red Red Red Red Red Red Red Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Red Green Green Green Green Green Red Green Green Green Green Green Pink Pink Pink Green Green Green Green
Row 3: Green Green Red Green Green Green Green Green Red Green Green Green Green Green Pink Green Pink Green Green Green Green
Row 4: Green Green Red Green Green Green Green Green Red Green Green Green Green Green Pink Pink Pink Green Green Green Green
Row 5: Green Green Red Red Red Red Red Red Red Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Purple Purple Purple Purple Purple Purple Green Blue Blue Blue Green Green Green Green Green Green Green
Row 7: Gray Gray Gray Green Purple Green Green Green Green Purple Green Blue Green Blue Green Green Green Green Green Green Green
Row 8: Gray Green Gray Green Purple Green Green Green Green Purple Green Blue Green Blue Green Green Green Green Green Green Green
Row 9: Gray Gray Gray Green Purple Green Green Green Green Purple Green Blue Blue Blue Green Green Green Green Green Green Green
Row 10: Green Green Green Green Purple Green Green Green Green Purple Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Purple Purple Purple Purple Purple Purple Black Black Black Black Black Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Black Green Green Green Black Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Black Green Green Green Black Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Black Green Green Green Black Green Green Green Green Green Green
Row 15: Green Orange Orange Orange Orange Green Green Green Green Green Black Green Green Green Black Green Green Green Green Green Green
Row 16: Green Orange Green Green Orange Green Green Green Green Green Black Black Black Black Black Green Brown Brown Brown Green Green
Row 17: Green Orange Green Green Orange Green Green Green Green Green Green Green Green Green Green Green Brown Green Brown Green Green
Row 18: Green Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Brown Green Brown Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Green Brown Brown Brown Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Yellow Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple
Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Brown Brown Brown Brown Yellow
Row 2: Black Brown Brown Brown Brown Green
Row 3: Blue Brown Brown Brown Brown Blue
Row 4: Orange Brown Brown Brown Brown Orange
Row 5: Blue Brown Brown Brown Brown Blue
Row 6: Brown Brown Brown Brown Brown Brown
Row 7: Purple Brown Brown Brown Brown Purple
Row 8: Black Brown Brown Brown Brown Black
Row 9: Red Brown Brown Brown Brown Red
Row 10: Purple Brown Brown Brown Brown Purple
Row 11: Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown
Row 13: Purple Brown Brown Brown Brown Purple
Row 14: Green Brown Brown Brown Brown Green
Row 15: Green Brown Brown Brown Brown Green
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Black Brown Brown Brown Brown Green
Row 3: Blue Blue Blue Blue Blue Blue
Row 4: Orange Orange Orange Orange Orange Orange
Row 5: Blue Blue Blue Blue Blue Blue
Row 6: Brown Brown Brown Brown Brown Brown
Row 7: Purple Purple Purple Purple Purple Purple
Row 8: Black Black Black Black Black Black
Row 9: Red Red Red Red Red Red
Row 10: Purple Purple Purple Purple Purple Purple
Row 11: Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown
Row 13: Purple Purple Purple Purple Purple Purple
Row 14: Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green
Example 2
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Brown
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Green Red Red Red Red Red Red Red Red Red Red Red Red Red Green
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Output:
Row 1: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 2: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 3: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 4: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 5: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 6: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 7: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 8: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 9: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 10: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 11: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 12: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 13: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 14: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 15: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 16: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 17: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Row 18: Green Purple Pink Black Red Gray Pink Purple Purple Gray Purple Purple Orange Purple Gray Purple Green Gray Purple Purple Black Red Black Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink
Row 2: Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Purple
Row 3: Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow
Row 4: Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Purple
Row 5: Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Purple
Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow
Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Purple
Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Green Orange Orange Orange Orange Black Orange Orange Orange Orange Green Black Orange Brown Orange Green Orange Black Orange Brown Orange Green Purple Black Purple Orange Orange
Row 2: Brown Black Orange Green Green Black Orange Black Orange Purple Orange Black Green Black Green Purple Orange Black Orange Black Green Orange Orange Black Orange Black Orange Orange
Row 3: Purple Orange Black Orange Black Brown Orange Orange Black Orange Black Brown Brown Brown Black Brown Black Brown Orange Orange Black Orange Black Orange Orange Orange Black Purple
Row 4: Purple Orange Orange Black Orange Brown Purple Orange Green Black Purple Green Orange Orange Orange Black Orange Orange Orange Orange Orange Black Orange Green Brown Orange Orange Black
Output:
Row 1: Black Green Orange Orange Orange Orange Black Yellow Yellow Yellow Yellow Yellow Black Orange Brown Orange Green Orange Black Orange Brown Orange Green Purple Black Yellow Yellow Yellow
Row 2: Yellow Black Orange Green Green Black Orange Black Yellow Yellow Yellow Black Green Black Green Purple Orange Black Yellow Black Green Orange Orange Black Orange Black Yellow Yellow
Row 3: Yellow Yellow Black Orange Black Brown Orange Orange Black Yellow Black Brown Brown Brown Black Brown Black Yellow Yellow Yellow Black Orange Black Orange Orange Orange Black Yellow
Row 4: Yellow Yellow Yellow Black Orange Brown Purple Orange Green Black Purple Green Orange Orange Orange Black Yellow Yellow Yellow Yellow Yellow Black Orange Green Brown Orange Orange Black
Example 2
Input:
Row 1: Black Orange Orange Pink Blue Orange Black Gray Blue Orange Gray Gray Black Pink Pink Blue Orange Pink Black Blue Blue Orange Orange Gray
Row 2: Pink Black Blue Gray Pink Black Blue Black Blue Blue Orange Black Pink Black Gray Pink Pink Black Blue Black Gray Gray Gray Black
Row 3: Pink Gray Black Gray Black Orange Pink Blue Black Orange Black Pink Orange Orange Black Blue Black Orange Blue Orange Black Orange Black Orange
Row 4: Gray Pink Gray Black Blue Pink Gray Orange Gray Black Blue Pink Orange Gray Blue Black Blue Gray Gray Gray Orange Black Pink Blue
Output:
Row 1: Black Orange Orange Pink Blue Orange Black Yellow Yellow Yellow Yellow Yellow Black Pink Pink Blue Orange Pink Black Blue Blue Orange Orange Gray
Row 2: Yellow Black Blue Gray Pink Black Blue Black Yellow Yellow Yellow Black Pink Black Gray Pink Pink Black Yellow Black Gray Gray Gray Black
Row 3: Yellow Yellow Black Gray Black Orange Pink Blue Black Yellow Black Pink Orange Orange Black Blue Black Yellow Yellow Yellow Black Orange Black Orange
Row 4: Yellow Yellow Yellow Black Blue Pink Gray Orange Gray Black Blue Pink Orange Gray Blue Black Yellow Yellow Yellow Yellow Yellow Black Pink Blue
Example 3
Input:
Row 1: Pink Gray Red Red Gray Gray Gray Gray Red Gray Pink Red Red Red
Row 2: Red Pink Red Gray Gray Red Red Gray Gray Pink Red Pink Gray Gray
Row 3: Gray Gray Pink Gray Red Gray Red Gray Pink Red Purple Red Pink Red
Row 4: Red Gray Gray Pink Red Red Gray Pink Red Red Red Gray Gray Pink
Row 5: Red Red Gray Gray Pink Red Pink Gray Red Red Red Red Red Red
Row 6: Gray Gray Gray Gray Gray Pink Red Purple Gray Purple Red Gray Red Gray
Output:
Row 1: Pink Gray Red Red Gray Gray Gray Gray Red Gray Pink Yellow Yellow Yellow
Row 2: Yellow Pink Red Gray Gray Red Red Gray Gray Pink Red Pink Yellow Yellow
Row 3: Yellow Yellow Pink Gray Red Gray Red Gray Pink Red Purple Red Pink Yellow
Row 4: Yellow Yellow Yellow Pink Red Red Gray Pink Red Red Red Gray Gray Pink
Row 5: Yellow Yellow Yellow Yellow Pink Red Pink Gray Red Red Red Red Red Red
Row 6: Yellow Yellow Yellow Yellow Yellow Pink Red Purple Gray Purple Red Gray Red Gray
Here is the input grid for the test example:
Input:
Row 1: Brown Pink Black Black Pink Pink Green Black Brown Black Black Black Black Black Black Orange Brown
Row 2: Black Brown Black Black Black Black Black Brown Black Brown Red Green Pink Black Black Brown Black
Row 3: Black Black Brown Red Black Black Brown Black Black Red Brown Black Black Black Brown Black Black
Row 4: Black Black Black Brown Black Brown Black Black Orange Black Black Brown Black Brown Black Green Black
Row 5: Black Black Orange Black Brown Black Black Black Black Black Black Black Brown Black Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Pink Black Black Pink Pink Green Black Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown
Yellow Brown Black Black Black Black Black Brown Black Brown Yellow Yellow Yellow Yellow Yellow Brown Black
Yellow Yellow Brown Red Black Black Brown Black Black Red Brown Yellow Yellow Yellow Brown Black Black
Yellow Yellow Yellow Brown Black Brown Black Black Orange Black Black Brown Yellow Brown Black Green Black
Yellow Yellow Yellow Yellow Brown Black Black Black Black Black Black Black Brown Black Black Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Red Blue Blue
Output:
Row 1: Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Blue Blue Blue
Row 2: Purple Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Red Blue Blue
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Red Red Red Purple Purple Purple Purple Red Purple Red Red Red Red Purple Red Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Gray Gray Gray
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Gray Gray Gray Gray Gray
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Gray Gray Gray Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Purple Gray Gray Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Purple Purple Gray Gray Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Gray Purple Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Red Red Red Purple Purple Purple Purple Red Purple Red Red Red Red Purple Red Purple Purple
Example 3
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 21: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray
Row 24: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray
Row 26: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray
Row 27: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 28: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 29: Blue Blue Red Blue Red Blue Blue Blue Blue Blue Blue Blue Red Red Blue
Output:
Row 1: Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Blue
Row 3: Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray
Row 6: Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Gray Gray Gray Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray Blue Blue
Row 9: Blue Blue Blue Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue
Row 10: Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 21: Gray Gray Gray Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray Blue Blue
Row 22: Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue
Row 23: Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray
Row 24: Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray
Row 26: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray
Row 27: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 28: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 29: Blue Blue Red Blue Red Blue Blue Blue Blue Blue Blue Blue Red Red Blue
Here is the input grid for the test example:
Input:
Row 1: Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 21: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 26: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 27: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green Blue Blue
Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green Blue Blue
Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green Blue Blue
Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green Blue Blue
Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green Blue Blue
Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green Blue Blue
Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green Blue Blue
Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green Blue Blue
Red Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green Blue
Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green Blue
Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green Blue
Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green Blue
Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green Blue
Red Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green
Blue Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green
Blue Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green
Blue Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green
Blue Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green
Blue Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue Green
Red Blue Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue
Blue Blue Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue
Blue Blue Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue
Blue Blue Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue
Blue Blue Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue
Blue Blue Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue
Blue Blue Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue
Blue Blue Blue Blue Green Blue Blue Green Blue Blue Green Green Green Blue Blue Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 27: Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink
Row 2: Pink Pink Orange Pink Orange Pink Orange Pink Orange Pink
Row 3: Orange Orange Orange Pink Orange Pink Orange Pink Orange Pink
Row 4: Pink Pink Pink Pink Orange Pink Orange Pink Orange Pink
Row 5: Orange Orange Orange Orange Orange Pink Orange Pink Orange Pink
Row 6: Pink Pink Pink Pink Pink Pink Orange Pink Orange Pink
Row 7: Orange Orange Orange Orange Orange Orange Orange Pink Orange Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink
Row 21: Blue Blue Blue Blue Blue Blue Blue Pink Blue Pink
Row 22: Pink Pink Pink Pink Pink Pink Blue Pink Blue Pink
Row 23: Blue Blue Blue Blue Blue Pink Blue Pink Blue Pink
Row 24: Pink Pink Pink Pink Blue Pink Blue Pink Blue Pink
Row 25: Blue Blue Blue Pink Blue Pink Blue Pink Blue Pink
Row 26: Pink Pink Blue Pink Blue Pink Blue Pink Blue Pink
Row 27: Blue Pink Blue Pink Blue Pink Blue Pink Blue Pink
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Pink Black Pink Black Pink Black Pink Black Pink Black Pink Black Pink
Row 2: Orange Orange Orange Orange Orange Black Black Pink Black Pink Black Pink Black Pink Black Pink Black Black
Row 3: Black Black Black Black Black Black Black Pink Black Pink Black Pink Black Pink Black Pink Pink Pink
Row 4: Orange Orange Orange Orange Orange Orange Orange Black Black Pink Black Pink Black Pink Black Black Black Black
Row 5: Black Black Black Black Black Black Orange Black Black Pink Black Pink Black Pink Pink Pink Pink Pink
Row 6: Orange Orange Orange Orange Orange Black Orange Black Orange Black Black Pink Black Black Black Black Black Black
Row 7: Black Black Black Black Orange Black Orange Black Orange Black Black Pink Pink Pink Pink Pink Pink Pink
Row 8: Orange Orange Orange Black Orange Black Orange Black Orange Black Orange Black Black Black Black Black Black Black
Row 9: Black Black Orange Black Orange Black Orange Black Orange Black Orange Black Black Pink Pink Pink Pink Pink
Row 10: Orange Black Orange Black Orange Black Orange Black Orange Black Orange Black Orange Black Black Black Black Black
Example 3
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray
Output:
Row 1: Black Black Black Black Black Black Green Black Green Black Green Black Black Gray Black Gray Black Gray Black Black Black Black Black Black
Row 2: Green Green Green Green Green Black Green Black Green Black Green Black Black Gray Black Gray Black Gray Black Gray Gray Gray Gray Gray
Row 3: Black Black Black Black Green Black Green Black Green Black Green Black Black Gray Black Gray Black Gray Black Gray Black Black Black Black
Row 4: Green Green Green Black Green Black Green Black Green Black Green Black Black Gray Black Gray Black Gray Black Gray Black Gray Gray Gray
Row 5: Black Black Green Black Green Black Green Black Green Black Green Black Black Gray Black Gray Black Gray Black Gray Black Gray Black Black
Row 6: Green Black Green Black Green Black Green Black Green Black Green Black Black Gray Black Gray Black Gray Black Gray Black Gray Black Gray
Here is the input grid for the test example:
Input:
Row 1: Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Purple Pink Purple Pink Purple Pink Purple Pink Purple Pink Purple
Pink Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Purple Pink Purple Pink Purple Pink Purple Pink Purple Pink Pink
Orange Orange Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Purple Pink Purple Pink Purple Pink Purple Pink Purple Purple Purple
Pink Pink Pink Pink Orange Pink Orange Pink Orange Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Orange Orange Orange Orange Pink Orange Pink Orange Pink Pink Pink Black Pink Black Pink Black Pink Black Pink Black Black Black
Pink Pink Pink Pink Pink Pink Orange Pink Orange Pink Black Pink Black Pink Black Pink Black Pink Black Pink Black Pink Pink
Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Black Pink Black Pink Black Pink Black Pink Black Pink Black Pink Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow
Row 3: Blue Blue Yellow Yellow
Row 4: Yellow Black Yellow Yellow
Output:
Row 1: Blue Blue Blue Blue
Row 2: Yellow Black Yellow Black
Row 3: Yellow Yellow Blue Blue
Row 4: Yellow Yellow Yellow Black
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Red Green
Row 8: Brown Brown Brown Brown Brown Brown Brown Pink Red
Row 9: Brown Brown Brown Brown Brown Brown Orange Brown Yellow
Output:
Row 1: Brown Brown Brown Brown Red Green Brown Red Green
Row 2: Brown Brown Brown Brown Pink Red Brown Pink Red
Row 3: Brown Brown Brown Orange Brown Yellow Orange Brown Yellow
Row 4: Brown Brown Brown Brown Red Green Brown Red Green
Row 5: Brown Brown Brown Brown Pink Red Brown Pink Red
Row 6: Brown Brown Brown Orange Brown Yellow Orange Brown Yellow
Row 7: Brown Red Green Brown Brown Brown Brown Red Green
Row 8: Brown Pink Red Brown Brown Brown Brown Pink Red
Row 9: Orange Brown Yellow Brown Brown Brown Orange Brown Yellow
Example 3
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Pink Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Pink Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink
Row 12: Blue Pink Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Pink
Row 13: Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue Pink Blue Blue Pink
Row 16: Blue Blue Blue Blue Blue Pink Blue Pink Blue Blue Blue Blue Blue Pink Blue Pink
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Black Yellow Brown Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Red Red Green Green Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Yellow Gray Black Yellow Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 24: Purple Brown Black Yellow Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 25: Pink Pink Green Brown Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray
Red Red Green Green Red Red Red Green Green Red Red Red Green Green Red Red Red Green Green Red Red Red Green Green Red
Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown
Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown
Pink Pink Green Brown Green Pink Pink Green Brown Green Pink Pink Green Brown Green Pink Pink Green Brown Green Pink Pink Green Brown Green
Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray
Red Red Green Green Red Red Red Green Green Red Red Red Green Green Red Red Red Green Green Red Red Red Green Green Red
Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown
Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown
Pink Pink Green Brown Green Pink Pink Green Brown Green Pink Pink Green Brown Green Pink Pink Green Brown Green Pink Pink Green Brown Green
Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray
Red Red Green Green Red Red Red Green Green Red Red Red Green Green Red Red Red Green Green Red Red Red Green Green Red
Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown
Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown
Pink Pink Green Brown Green Pink Pink Green Brown Green Pink Pink Green Brown Green Pink Pink Green Brown Green Pink Pink Green Brown Green
Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray
Red Red Green Green Red Red Red Green Green Red Red Red Green Green Red Red Red Green Green Red Red Red Green Green Red
Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown
Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown
Pink Pink Green Brown Green Pink Pink Green Brown Green Pink Pink Green Brown Green Pink Pink Green Brown Green Pink Pink Green Brown Green
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray Black Yellow Brown Gray Gray
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Green Green Red Red Red Green Green Red Red Red Green Green Red
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown Yellow Gray Black Yellow Brown
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown Purple Brown Black Yellow Brown
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Brown Green Pink Pink Green Brown Green Pink Pink Green Brown Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Yellow Yellow
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 21: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 26: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Pink Yellow Yellow
Row 2: Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Purple Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Purple Pink Pink
Row 2: Pink Pink Pink
Row 3: Pink Pink Pink
Example 3
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 28: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Red Purple Black
Row 2: Blue Green Pink
Row 3: Purple Red Pink
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Orange Red Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Black Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Red Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Blue Green Red
Black Green Black Pink
Pink Green Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Orange Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Blue Blue Blue Orange Orange Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Yellow Blue Yellow Blue Blue Blue Blue Blue Pink Pink Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue
Row 11: Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Red Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Red Blue
Row 2: Blue Blue Red
Row 3: Red Blue Red
Row 4: Blue Red Blue
Example 2
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Purple Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Purple Green Purple Purple Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Purple Purple Purple Green Green Purple Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Purple Purple Green Green Green Purple Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Yellow Yellow Yellow Green Green Green Green Green Green Green Green Purple Purple Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Yellow Gray Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Green Orange Orange Orange Green Green Green Black Black
Row 10: Green Green Green Green Green Green Green Purple Green Green Brown Brown Brown Green Green Orange Orange Orange Orange Orange Green Green Green Black Black
Row 11: Green Green Green Green Green Purple Purple Purple Green Brown Brown Brown Brown Brown Green Orange Orange Orange Orange Orange Green Green Green Black Black
Row 12: Green Black Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange Green Orange Orange Green Green Green Black Black
Row 13: Green Black Black Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange Orange Orange Orange Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow
Example 3
Input:
Row 1: Black Black Black Green Black Black Gray Black Gray Black Gray Black Black Black Black Black Black Green Green Green Black Black Black
Row 2: Black Green Green Green Black Black Gray Gray Gray Gray Black Black Black Black Black Black Black Green Black Black Black Black Black
Row 3: Black Green Green Green Green Black Black Gray Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Green Black Black Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Brown Brown Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Brown Brown Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Brown Brown Brown Black Black Black Black Orange Black Black Black Black Black Gray Gray Gray Black
Row 9: Black Black Black Black Yellow Black Black Black Black Black Black Orange Orange Orange Black Black Black Black Black Gray Gray Gray Black
Row 10: Black Black Yellow Yellow Black Black Black Black Black Black Black Orange Orange Orange Black Black Black Black Black Gray Gray Gray Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Black Black Black Black Pink Black Black Pink Pink Black Black
Row 13: Black Yellow Yellow Yellow Yellow Yellow Black Brown Brown Brown Brown Black Brown Black Black Black Black Pink Pink Pink Pink Black Black
Row 14: Black Yellow Black Yellow Yellow Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Black Purple Purple Black Black Black Black Black Black Black Black
Row 16: Black Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Black Purple Purple Black Black Purple Purple Purple Purple Purple Black
Row 17: Black Yellow Yellow Yellow Yellow Black Black Black Black Black Black Black Black Purple Purple Black Black Purple Purple Purple Purple Purple Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Black
Row 19: Green Black Green Green Green Green Black Black Black Black Red Red Black Black Black Black Black Black Black Black Black Black Black
Row 20: Green Green Green Green Black Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Pink Pink
Row 21: Black Black Black Black Black Black Black Black Black Black Red Black Blue Blue Black Black Black Black Black Black Black Pink Pink
Row 22: Black Black Black Black Black Black Black Black Black Black Red Black Blue Blue Black Black Black Black Black Black Black Pink Pink
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Yellow Yellow Black Black Black Black Pink Black
Row 24: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black
Row 25: Black Pink Black Pink Pink Pink Pink Black Black Black Black Black Black Black Black Yellow Yellow Black Black Black Black Black Black
Row 26: Black Pink Pink Pink Pink Pink Pink Black Black Black Black Black Black Black Black Yellow Black Black Black Black Black Black Black
Row 27: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Yellow Yellow Black Black Black Black Black Black
Row 28: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Pink Black Black
Row 29: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Pink Pink Black
Output:
Row 1: Yellow Yellow
Row 2: Black Yellow
Row 3: Yellow Yellow
Row 4: Yellow Black
Row 5: Yellow Yellow
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown
Row 3: Red Yellow Red Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Red Red Red Red Red Brown Brown Brown Brown Brown Pink Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Purple Brown Brown Pink Brown Brown Brown Brown
Row 8: Green Green Brown Brown Brown Brown Purple Brown Brown Pink Brown Brown Brown Brown
Row 9: Green Brown Brown Brown Brown Brown Purple Brown Brown Brown Pink Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Red Red Brown Red
Red Red Red Red Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Blue Blue Blue
Row 2: Yellow Yellow Blue Blue
Row 3: Yellow Yellow Blue Blue
Row 4: Blue Blue Blue Blue
Row 5: Blue Yellow Blue Blue
Row 6: Orange Orange Orange Orange
Row 7: Blue Red Red Blue
Row 8: Red Red Red Red
Row 9: Red Red Red Red
Row 10: Red Red Blue Red
Row 11: Red Red Blue Blue
Output:
Row 1: Blue Green Green Blue
Row 2: Green Green Green Green
Row 3: Green Green Green Green
Row 4: Green Green Blue Green
Row 5: Green Green Blue Blue
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Gray Brown Brown Brown Brown Brown Gray Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Gray Gray Brown Brown Brown Brown Brown Brown Gray Brown Brown Gray Brown Gray Brown Brown Brown Brown Brown Brown Gray
Row 11: Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Green Brown Green Brown Brown Brown Green Brown
Row 2: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Green Green Brown Brown Brown Brown Brown Brown Green Brown Brown Green Brown Green Brown Brown Brown Brown Brown Green Green
Row 5: Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Black Brown
Row 3: Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown
Row 6: Black Brown Brown Brown Brown
Row 7: Black Brown Brown Black Brown
Row 8: Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Black Black
Row 10: Black Brown Brown Brown Black
Row 11: Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown
Row 14: Pink Pink Pink Pink Pink
Row 15: Brown Brown Gray Gray Gray
Row 16: Gray Brown Brown Brown Brown
Row 17: Gray Brown Gray Brown Gray
Row 18: Gray Brown Gray Gray Gray
Row 19: Gray Gray Gray Gray Brown
Row 20: Brown Gray Brown Gray Gray
Row 21: Brown Gray Brown Gray Gray
Row 22: Brown Gray Brown Brown Gray
Row 23: Gray Gray Gray Gray Gray
Row 24: Brown Gray Gray Gray Gray
Row 25: Gray Gray Brown Gray Brown
Row 26: Brown Gray Gray Brown Gray
Row 27: Brown Gray Brown Gray Gray
Output:
Row 1: Brown Brown Green Green Green
Row 2: Green Brown Brown Green Brown
Row 3: Green Brown Green Brown Green
Row 4: Green Brown Green Green Green
Row 5: Green Green Green Green Brown
Row 6: Green Green Brown Green Green
Row 7: Green Green Brown Green Green
Row 8: Brown Green Brown Brown Green
Row 9: Green Green Green Green Green
Row 10: Green Green Green Green Green
Row 11: Green Green Brown Green Brown
Row 12: Brown Green Green Brown Green
Row 13: Brown Green Brown Green Green
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Blue
Row 2: Yellow Blue Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Blue Blue
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Red Red Red Red Red Red
Row 6: Yellow Yellow Black Black Black Black
Row 7: Black Black Black Yellow Black Yellow
Row 8: Black Yellow Yellow Black Black Yellow
Row 9: Black Yellow Yellow Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Yellow Yellow Green Green Green Green
Green Green Green Yellow Green Yellow
Green Yellow Yellow Green Green Green
Green Yellow Yellow Green Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Black Black Black Black Black Black Green Green Green Green Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Green Black Black Black Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Green Black Black Black Green Black Black Black Black Black Black Black Black Black Green Green Green Green Green Black Black Black
Row 4: Black Black Black Black Black Black Black Black Green Black Black Black Green Green Green Green Green Green Black Black Black Black Green Black Black Black Green Black Black Black
Row 5: Black Black Black Black Black Black Black Black Green Green Green Green Green Green Black Black Black Green Black Black Black Black Green Black Black Black Green Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black Green Black Black Black Black Green Black Black Black Green Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black Green Black Black Black Black Green Green Green Green Green Black Black Black
Row 8: Black Black Black Black Black Green Green Green Green Green Black Black Black Green Green Green Green Green Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Green Black Black Black Green Black Black Black Black Black Black Black Black Green Green Green Green Green Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Green Black Black Black Green Black Black Black Black Black Black Black Black Green Black Black Black Green Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Green Black Black Black Green Black Black Black Black Black Black Black Black Green Black Black Black Green Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Green Green Green Green Green Black Black Black Black Black Black Black Black Green Black Black Black Green Green Green Green Green Green Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Green Green Green Green Green Black Black Black Green Black Black
Row 14: Black Black Black Black Black Black Black Black Green Green Green Green Green Black Black Black Black Black Black Black Black Black Black Green Black Black Black Green Black Black
Row 15: Black Black Black Black Black Black Black Black Green Black Black Black Green Black Black Black Black Black Black Black Black Black Black Green Black Black Black Green Black Black
Row 16: Green Green Green Green Green Black Black Black Green Black Black Black Green Black Black Black Black Black Black Black Black Black Black Green Green Green Green Green Black Black
Row 17: Green Black Black Black Green Black Black Black Green Black Black Black Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Green Black Black Black Green Black Black Black Green Green Green Green Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Green Black Black Black Green Black Black Black Black Black Black Black Black Black Black Black Green Green Green Green Green Black Black Black Black Black Black Black Black Black
Row 20: Green Green Green Green Green Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black Green Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black Green Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black Green Green Green Green Green Green Black Black Black Black
Row 23: Black Black Black Black Black Green Green Green Green Green Black Green Green Green Green Green Green Green Green Green Green Green Black Black Black Green Black Black Black Black
Row 24: Black Black Black Black Black Green Black Black Black Green Black Green Black Black Black Green Black Black Black Black Black Green Black Black Black Green Black Black Black Black
Row 25: Black Black Black Black Black Green Black Black Black Green Black Green Black Black Black Green Black Black Black Black Black Green Black Black Black Green Black Black Black Black
Row 26: Black Black Black Black Black Green Black Black Black Green Black Green Black Black Black Green Black Black Black Black Black Green Green Green Green Green Black Black Black Black
Row 27: Black Black Black Black Black Green Green Green Green Green Black Green Green Green Green Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Pink Black Black Black Black Pink Green Green Green Green Green Pink Black Pink Black Black Pink Black Pink Black Black Pink Pink Pink Black Black Black Black
Row 2: Black Black Pink Black Black Black Black Pink Green Black Pink Black Green Pink Black Pink Black Black Pink Black Pink Black Black Pink Pink Pink Black Black Black Black
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Pink Pink Pink
Row 4: Black Black Pink Black Black Black Black Pink Green Black Pink Black Green Green Green Green Green Green Pink Black Pink Black Green Pink Pink Pink Green Black Black Black
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Green Pink Pink Pink Green Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink
Row 7: Black Black Pink Black Black Black Black Pink Black Black Pink Black Black Green Black Pink Black Green Pink Black Pink Black Green Green Green Green Green Black Black Black
Row 8: Black Black Pink Black Black Green Green Green Green Green Pink Black Black Green Green Green Green Green Pink Black Pink Black Black Pink Pink Pink Black Black Black Black
Row 9: Black Black Pink Black Black Green Black Pink Black Green Pink Black Black Pink Black Pink Black Black Green Green Green Green Green Pink Pink Pink Black Black Black Black
Row 10: Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink
Row 12: Black Black Pink Black Black Green Green Green Green Green Pink Black Black Pink Black Pink Black Black Green Black Pink Black Green Green Green Green Green Green Black Black
Row 13: Black Black Pink Black Black Black Black Pink Black Black Pink Black Black Pink Black Pink Black Black Green Green Green Green Green Green Pink Pink Black Green Black Black
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink
Row 15: Black Black Pink Black Black Black Black Pink Green Black Pink Black Green Pink Black Pink Black Black Pink Black Pink Black Black Green Pink Pink Black Green Black Black
Row 16: Green Green Green Green Green Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Pink Pink
Row 17: Green Black Pink Black Green Black Black Pink Green Black Pink Black Green Pink Black Pink Black Black Pink Black Pink Black Black Pink Pink Pink Black Black Black Black
Row 18: Green Pink Pink Pink Green Pink Pink Pink Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Green Black Pink Black Green Black Black Pink Black Black Pink Black Black Pink Black Pink Green Green Green Green Green Black Black Pink Pink Pink Black Black Black Black
Row 20: Green Green Green Green Green Black Black Pink Black Black Pink Black Black Pink Black Pink Green Black Pink Black Green Black Black Pink Pink Pink Black Black Black Black
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Black Black Pink Black Black Black Black Pink Black Black Pink Black Black Pink Black Pink Green Black Pink Black Green Green Green Green Green Green Black Black Black Black
Row 23: Black Black Pink Black Black Green Green Green Green Green Pink Green Green Green Green Green Green Green Green Green Green Green Black Pink Pink Green Black Black Black Black
Row 24: Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink
Row 26: Black Black Pink Black Black Green Black Pink Black Green Pink Green Black Pink Black Green Black Black Pink Black Pink Green Green Green Green Green Black Black Black Black
Row 27: Black Black Pink Black Black Green Green Green Green Green Pink Green Green Green Green Green Black Black Pink Black Pink Black Black Pink Pink Pink Black Black Black Black
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Orange Orange Orange Orange Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Orange Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Black Black Black Black
Row 4: Orange Black Black Black Orange Black Black Black Black Orange Orange Orange Orange Orange Black Black Black Black Black Orange Black Black Black Orange Black Black Black Black
Row 5: Orange Black Black Black Orange Black Black Black Black Orange Black Black Black Orange Black Black Black Black Black Orange Black Black Black Orange Black Black Black Black
Row 6: Orange Orange Orange Orange Orange Black Black Black Black Orange Black Black Black Orange Black Black Black Black Black Orange Black Black Black Orange Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Orange Black Black Black Orange Black Black Black Black Black Orange Orange Orange Orange Orange Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Black Black
Row 9: Black Orange Orange Orange Orange Orange Black Black Black Black Orange Orange Orange Orange Orange Black Black Black Black Black Black Orange Black Black Black Orange Black Black
Row 10: Black Orange Black Black Black Orange Black Black Black Black Orange Black Black Black Orange Black Black Black Black Black Black Orange Black Black Black Orange Black Black
Row 11: Black Orange Black Black Black Orange Black Black Black Black Orange Black Black Black Orange Black Black Black Black Black Black Orange Black Black Black Orange Black Black
Row 12: Black Orange Black Black Black Orange Black Black Black Black Orange Black Black Black Orange Black Black Black Black Black Black Orange Orange Orange Orange Orange Black Black
Row 13: Black Orange Orange Orange Orange Orange Black Black Black Black Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Black Black Black Black Black Black Black
Row 14: Orange Orange Orange Orange Orange Black Black Black Orange Orange Orange Orange Orange Black Black Black Orange Black Black Black Orange Black Black Black Black Black Black Black
Row 15: Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Black Black Black Black
Row 16: Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Black Black Black Black
Row 17: Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Orange Orange Orange Orange Black Black Black Black Black Black Black
Row 18: Orange Orange Orange Orange Orange Black Black Black Orange Orange Orange Orange Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Pink Pink Black Black Black Black Black Black Pink Pink Pink Black Black Black Black Black Pink Black Black Pink Black Pink Black Black Black Black
Row 2: Orange Orange Orange Orange Orange Black Black Black Black Black Pink Pink Pink Black Black Black Black Black Pink Black Black Pink Black Pink Black Black Black Black
Row 3: Orange Black Pink Pink Orange Black Black Black Black Black Pink Pink Pink Black Black Black Black Black Pink Orange Orange Orange Orange Orange Black Black Black Black
Row 4: Orange Pink Pink Pink Orange Pink Pink Pink Pink Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Pink
Row 5: Orange Pink Pink Pink Orange Pink Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Pink
Row 6: Orange Orange Orange Orange Orange Pink Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Pink
Row 7: Black Black Pink Pink Black Black Black Black Black Orange Pink Pink Pink Orange Black Black Black Black Pink Orange Orange Orange Orange Orange Black Black Black Black
Row 8: Black Black Pink Pink Black Black Black Black Black Orange Orange Orange Orange Orange Black Black Black Black Pink Black Black Orange Orange Orange Orange Orange Black Black
Row 9: Black Orange Orange Orange Orange Orange Black Black Black Black Orange Orange Orange Orange Orange Black Black Black Pink Black Black Orange Black Pink Black Orange Black Black
Row 10: Pink Orange Pink Pink Pink Orange Pink Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink
Row 11: Pink Orange Pink Pink Pink Orange Pink Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink
Row 12: Black Orange Pink Pink Black Orange Black Black Black Black Orange Pink Pink Black Orange Black Black Black Pink Black Black Orange Orange Orange Orange Orange Black Black
Row 13: Black Orange Orange Orange Orange Orange Black Black Black Black Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Pink Black Pink Black Black Black Black
Row 14: Orange Orange Orange Orange Orange Black Black Black Orange Orange Orange Orange Orange Black Black Black Orange Black Pink Black Orange Pink Black Pink Black Black Black Black
Row 15: Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink
Row 16: Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink
Row 17: Orange Black Pink Pink Orange Black Black Black Orange Black Pink Pink Orange Black Black Black Orange Orange Orange Orange Orange Pink Black Pink Black Black Black Black
Row 18: Orange Orange Orange Orange Orange Black Black Black Orange Orange Orange Orange Orange Black Black Black Black Black Pink Black Black Pink Black Pink Black Black Black Black
Example 3
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Red Red Red Red Red Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Red Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Red Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Red Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Red Blue Blue Blue Red Blue Red Red Red Red Red Red Blue Blue Blue Red Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Red Blue Blue Blue Red Blue Red Blue Blue Blue Red Red Red Red Red Red Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Red Red Red Red Red Blue Red Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Red Red Red Red Red Blue Blue Blue Blue Blue Red Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Red Blue Blue Blue Red Blue Blue Blue Blue Blue Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Red Blue Blue Blue Red Blue Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Red Blue Blue Blue Red Blue Red Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Red Red Red Red Red Blue Blue Blue
Row 11: Red Red Red Red Red Blue Red Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Red Blue Blue Blue
Row 12: Red Red Red Red Red Blue Red Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Red Blue Blue Blue
Row 13: Red Blue Blue Blue Red Blue Red Red Red Red Red Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Red Blue Blue Blue
Row 14: Red Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Blue Blue Blue
Row 15: Red Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Pink Blue Blue Blue Pink Blue Pink Blue Blue Blue Pink Blue Blue Red Red Red Red Red Blue Blue Blue Blue Blue
Row 2: Blue Blue Pink Blue Red Red Red Red Red Blue Blue Blue Pink Blue Blue Red Blue Pink Blue Red Blue Blue Blue Blue Blue
Row 3: Pink Pink Pink Pink Red Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Red Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Red Pink Pink Pink Red Pink Red Red Red Red Red Red Pink Pink Pink Red Pink Pink Pink Pink Pink
Row 5: Blue Blue Pink Blue Red Blue Pink Blue Red Blue Red Blue Pink Blue Red Red Red Red Red Red Blue Blue Blue Blue Blue
Row 6: Pink Pink Pink Pink Red Red Red Red Red Pink Red Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Red Red Red Red Red Blue Pink Blue Pink Blue Red Blue Pink Blue Red Blue Blue Pink Blue Pink Blue Blue Blue Blue Blue
Row 8: Red Blue Pink Blue Red Blue Pink Blue Pink Blue Red Red Red Red Red Blue Blue Pink Blue Pink Blue Blue Blue Blue Blue
Row 9: Red Pink Pink Pink Red Pink Red Red Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Red Blue Pink Blue Red Blue Red Blue Pink Blue Red Blue Pink Blue Blue Blue Blue Red Red Red Red Red Blue Blue Blue
Row 11: Red Red Red Red Red Pink Red Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Red Pink Pink Pink
Row 12: Red Red Red Red Red Pink Red Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Red Pink Pink Pink
Row 13: Red Blue Pink Blue Red Blue Red Red Red Red Red Blue Pink Blue Blue Blue Blue Red Blue Pink Blue Red Blue Blue Blue
Row 14: Red Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Pink Pink Pink
Row 15: Red Blue Pink Blue Red Blue Pink Blue Pink Blue Blue Blue Pink Blue Blue Blue Blue Pink Blue Pink Blue Blue Blue Blue Blue
Row 16: Red Red Red Red Red Blue Pink Blue Pink Blue Blue Blue Pink Blue Blue Blue Blue Pink Blue Pink Blue Blue Blue Blue Blue
Row 17: Blue Blue Pink Blue Blue Blue Pink Blue Pink Blue Blue Blue Pink Blue Blue Blue Blue Pink Blue Pink Blue Blue Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray Orange Orange Orange Gray Orange
Row 5: Gray Orange Orange Orange Gray Gray Orange Orange Orange Gray Orange Orange Gray Gray Gray Gray Gray Orange
Row 6: Gray Orange Orange Orange Gray Gray Orange Orange Orange Gray Orange Gray Gray Gray Gray Gray Orange Orange
Row 7: Gray Orange Orange Orange Gray Gray Orange Orange Orange Gray Orange Gray Orange Orange Orange Gray Orange Orange
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Orange Orange Orange Gray Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Gray Orange Orange Orange Gray Orange Orange Orange Orange Gray Gray Gray Gray Gray Orange Orange Orange Orange
Row 15: Gray Orange Orange Orange Gray Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange Orange Orange
Row 16: Gray Orange Orange Orange Gray Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange Orange Orange
Row 17: Gray Gray Gray Gray Gray Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange Orange Orange
Row 18: Gray Gray Gray Gray Gray Orange Orange Orange Orange Gray Gray Gray Gray Gray Orange Orange Orange Orange
Row 19: Gray Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Gray Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Gray Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Orange Pink Orange Orange Orange Orange Pink Orange Orange Orange Pink Gray Gray Gray Gray Gray Orange
Orange Orange Pink Orange Orange Orange Orange Pink Orange Orange Orange Pink Gray Pink Pink Orange Gray Orange
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Gray Pink
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Pink Gray Pink Pink Orange Gray Orange
Gray Orange Pink Orange Gray Gray Orange Pink Orange Gray Orange Pink Gray Gray Gray Gray Gray Orange
Gray Pink Pink Pink Gray Gray Pink Pink Pink Gray Pink Gray Gray Gray Gray Gray Pink Pink
Gray Orange Pink Orange Gray Gray Orange Pink Orange Gray Orange Gray Orange Pink Pink Gray Orange Orange
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Pink Pink Pink Gray Pink Pink
Orange Orange Pink Orange Orange Orange Orange Pink Orange Orange Orange Gray Orange Pink Pink Gray Orange Orange
Orange Orange Pink Orange Orange Orange Orange Pink Orange Orange Orange Gray Gray Gray Gray Gray Orange Orange
Orange Orange Pink Orange Orange Orange Orange Pink Orange Orange Orange Pink Orange Pink Pink Orange Orange Orange
Orange Orange Pink Orange Orange Orange Orange Pink Orange Orange Orange Pink Orange Pink Pink Orange Orange Orange
Gray Gray Gray Gray Gray Orange Orange Pink Orange Orange Orange Pink Orange Pink Pink Orange Orange Orange
Gray Orange Pink Orange Gray Orange Orange Pink Orange Gray Gray Gray Gray Gray Pink Orange Orange Orange
Gray Pink Pink Pink Gray Pink Pink Pink Pink Gray Pink Pink Pink Gray Pink Pink Pink Pink
Gray Pink Pink Pink Gray Pink Pink Pink Pink Gray Pink Pink Pink Gray Pink Pink Pink Pink
Gray Gray Gray Gray Gray Orange Orange Pink Orange Gray Orange Pink Orange Gray Pink Orange Orange Orange
Gray Gray Gray Gray Gray Orange Orange Pink Orange Gray Gray Gray Gray Gray Pink Orange Orange Orange
Gray Orange Pink Orange Gray Orange Orange Pink Orange Orange Orange Pink Orange Pink Pink Orange Orange Orange
Gray Pink Pink Pink Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Gray Orange Pink Orange Gray Orange Orange Pink Orange Orange Orange Pink Orange Pink Pink Orange Orange Orange
Gray Gray Gray Gray Gray Orange Orange Pink Orange Orange Orange Pink Orange Pink Pink Orange Orange Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Black Blue Black Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Black Orange Orange Orange Orange Black Orange Orange Orange Orange
Row 13: Orange Black Blue Black Orange Orange Black Pink Black Orange Orange Orange
Row 14: Orange Orange Black Orange Orange Orange Orange Black Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Blue Orange Black Orange Blue Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Blue Black Blue Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Black Black Blue Black Black Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Blue Black Blue Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Blue Orange Black Orange Blue Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Blue Orange Black Orange Blue Pink Orange Black Orange Pink Orange Orange
Row 12: Orange Blue Black Blue Orange Orange Pink Black Pink Orange Orange Orange
Row 13: Black Black Blue Black Black Black Black Pink Black Black Orange Orange
Row 14: Orange Blue Black Blue Orange Orange Pink Black Pink Orange Orange Orange
Row 15: Blue Orange Black Orange Blue Pink Orange Black Orange Pink Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Brown Pink Brown Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Pink Orange Pink Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Brown Pink Brown Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue
Row 21: Blue Brown Gray Brown Blue Blue Blue Blue Blue Blue
Row 22: Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 26: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 27: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 28: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 29: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Pink Blue Brown Blue Pink Blue Blue
Row 3: Blue Blue Blue Blue Pink Brown Pink Blue Blue Blue
Row 4: Blue Blue Blue Brown Brown Pink Brown Brown Blue Blue
Row 5: Blue Blue Blue Blue Pink Brown Pink Blue Blue Blue
Row 6: Blue Blue Blue Pink Blue Brown Blue Pink Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Orange Blue Pink Blue Orange Blue
Row 9: Blue Blue Blue Blue Blue Orange Pink Orange Blue Blue
Row 10: Blue Blue Blue Blue Pink Pink Orange Pink Pink Blue
Row 11: Blue Blue Blue Blue Blue Orange Pink Orange Blue Blue
Row 12: Blue Blue Blue Blue Orange Blue Pink Blue Orange Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Pink Blue Brown Blue Pink Blue Blue Blue Blue Blue
Row 15: Blue Pink Brown Pink Blue Blue Blue Blue Blue Blue
Row 16: Brown Brown Pink Brown Brown Blue Blue Blue Blue Blue
Row 17: Blue Pink Brown Pink Blue Blue Blue Blue Blue Blue
Row 18: Pink Blue Brown Blue Pink Blue Blue Blue Blue Blue
Row 19: Gray Blue Brown Blue Gray Blue Blue Blue Blue Blue
Row 20: Blue Gray Brown Gray Blue Blue Blue Blue Blue Blue
Row 21: Brown Brown Gray Brown Brown Blue Blue Blue Blue Blue
Row 22: Blue Gray Brown Gray Blue Blue Blue Blue Blue Blue
Row 23: Gray Blue Brown Blue Gray Blue Blue Blue Blue Blue
Row 24: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 26: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 27: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 28: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 29: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Blue Pink Blue Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Blue Orange Blue Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Pink Blue Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Blue Brown Pink Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Orange Brown Blue Brown Orange Brown Pink Blue Pink Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Orange Blue Orange Brown Blue Blue Pink Blue Blue Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Blue Blue Orange Blue Blue Brown Pink Blue Pink Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Orange Blue Orange Brown Pink Brown Blue Brown Pink Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Orange Brown Blue Brown Orange Pink Brown Blue Brown Pink Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Blue Pink Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Pink Blue Blue Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Blue Pink Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Blue Brown Pink Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Here is the input grid for the test example:
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Gray Brown Gray Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Black Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Black Pink Black Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Black Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Pink Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Pink Gray Pink Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Pink Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 21: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 22: Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red
Row 23: Red Red Red Red Red Red Red Red Red Orange Black Orange Red Red Red
Row 24: Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red
Row 25: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 26: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 27: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 28: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 29: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Brown Red Gray Red Brown Red
Red Red Red Red Red Red Red Red Red Red Brown Gray Brown Red Red
Red Red Red Red Red Red Red Red Red Gray Gray Brown Gray Gray Red
Red Red Red Red Red Red Red Red Red Red Brown Gray Brown Red Red
Red Red Red Red Red Red Red Red Red Brown Red Gray Red Brown Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Pink Red Black Red Pink Red Red
Red Red Red Red Red Red Red Red Red Pink Black Pink Red Red Red
Red Red Red Red Red Red Red Red Black Black Pink Black Black Red Red
Red Red Red Red Red Red Red Red Red Pink Black Pink Red Red Red
Red Red Red Red Red Red Red Red Pink Red Black Red Pink Red Red
Red Red Red Red Gray Red Pink Red Gray Red Red Red Red Red Red
Red Red Red Red Red Gray Pink Gray Red Red Red Red Red Red Red
Red Red Red Red Pink Pink Gray Pink Pink Red Red Red Red Red Red
Red Red Red Red Red Gray Pink Gray Red Red Red Red Red Red Red
Red Red Red Red Gray Red Pink Red Gray Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Black Red Orange Red Black Red Red
Red Red Red Red Red Red Red Red Red Black Orange Black Red Red Red
Red Red Red Red Red Red Red Red Orange Orange Black Orange Orange Red Red
Red Red Red Red Red Red Red Red Red Black Orange Black Red Red Red
Red Red Red Red Red Red Red Red Black Red Orange Red Black Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray Gray Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray Gray Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray Gray Red Red Red Red Red
Row 8: Red Red Yellow Yellow Yellow Red Red Red Red Red Red Red Red Gray Gray Gray Gray Gray Green Green Green Green Red
Row 9: Red Red Yellow Yellow Yellow Red Red Red Red Red Red Red Red Gray Gray Gray Gray Gray Green Green Green Green Red
Row 10: Red Red Yellow Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Red
Row 11: Red Red Yellow Yellow Yellow Red Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Green Green Green Green Red
Row 12: Red Red Yellow Yellow Yellow Red Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Green Green Green Green Red
Row 13: Red Red Red Red Red Red Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Green Green Green Green Red
Row 14: Red Red Red Red Red Red Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray Gray Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Gray Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Gray Red Red Red Red Red
Row 8: Red Red Yellow Yellow Yellow Red Red Red Red Red Red Red Red Gray Red Red Red Gray Green Green Green Green Red
Row 9: Red Red Yellow Red Yellow Red Red Red Red Red Red Red Red Gray Gray Gray Gray Gray Green Red Red Green Red
Row 10: Red Red Yellow Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Green Red
Row 11: Red Red Yellow Red Yellow Red Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Green Red Red Green Red
Row 12: Red Red Yellow Yellow Yellow Red Pink Red Red Red Red Pink Red Red Red Red Red Red Green Red Red Green Red
Row 13: Red Red Red Red Red Red Pink Red Red Red Red Pink Red Red Red Red Red Red Green Green Green Green Red
Row 14: Red Red Red Red Red Red Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Example 2
Input:
Row 1: Yellow Yellow Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Green Green Green Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Yellow Yellow Gray Gray Gray Gray Yellow
Row 7: Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Yellow Yellow Gray Gray Gray Gray Yellow
Row 8: Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Yellow Yellow Gray Gray Gray Gray Yellow
Row 9: Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Yellow Yellow Gray Gray Gray Gray Yellow
Row 10: Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow
Row 15: Yellow Yellow Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow
Row 16: Yellow Yellow Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow
Row 17: Yellow Yellow Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow
Row 18: Yellow Yellow Red Red Red Red Red Yellow Brown Brown Brown Yellow Yellow Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow
Row 19: Yellow Yellow Red Red Red Red Red Yellow Brown Brown Brown Yellow Yellow Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow
Row 20: Yellow Yellow Red Red Red Red Red Yellow Brown Brown Brown Yellow Yellow Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Green Green Green Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Yellow Yellow Gray Gray Gray Gray Yellow
Row 7: Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Orange Yellow Yellow Yellow Orange Yellow Yellow Gray Yellow Yellow Gray Yellow
Row 8: Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Pink Orange Yellow Yellow Yellow Orange Yellow Yellow Gray Yellow Yellow Gray Yellow
Row 9: Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Pink Orange Yellow Yellow Yellow Orange Yellow Yellow Gray Gray Gray Gray Yellow
Row 10: Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Orange Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow
Row 15: Yellow Yellow Red Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Blue Yellow Yellow Yellow
Row 16: Yellow Yellow Red Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Blue Yellow Yellow Yellow
Row 17: Yellow Yellow Red Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Blue Yellow Yellow Yellow
Row 18: Yellow Yellow Red Yellow Yellow Yellow Red Yellow Brown Brown Brown Yellow Yellow Yellow Yellow Blue Yellow Yellow Blue Yellow Yellow Yellow
Row 19: Yellow Yellow Red Yellow Yellow Yellow Red Yellow Brown Yellow Brown Yellow Yellow Yellow Yellow Blue Yellow Yellow Blue Yellow Yellow Yellow
Row 20: Yellow Yellow Red Red Red Red Red Yellow Brown Yellow Brown Yellow Yellow Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 3
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red
Row 5: Red Red Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red
Row 6: Red Red Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red
Row 7: Red Red Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Gray Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Gray Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Gray Red Red Red Red Red Red Red Red Red
Row 5: Red Red Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Gray Red Red Gray Red Red Red Red Red Red Red Red Red
Row 6: Red Red Blue Red Red Red Blue Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red
Row 7: Red Red Blue Red Red Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Here is the input grid for the test example:
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Black Black Pink Pink Pink Pink Pink Black
Row 8: Black Red Red Red Red Red Red Red Black Black Black Black Black Brown Brown Brown Brown Brown Brown Black Black Pink Pink Pink Pink Pink Black
Row 9: Black Red Red Red Red Red Red Red Black Black Black Black Black Brown Brown Brown Brown Brown Brown Black Black Pink Pink Pink Pink Pink Black
Row 10: Black Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Black
Row 11: Black Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Brown Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Brown Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Brown Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Brown Black Black Pink Pink Pink Pink Pink Black
Black Red Red Red Red Red Red Red Black Black Black Black Black Brown Black Black Black Black Brown Black Black Pink Black Black Black Pink Black
Black Red Black Black Black Black Black Red Black Black Black Black Black Brown Brown Brown Brown Brown Brown Black Black Pink Black Black Black Pink Black
Black Red Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Pink Black
Black Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Pink Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Pink Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Yellow Gray Gray Yellow Gray Gray Yellow Gray Gray
Row 4: Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Yellow Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Yellow
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Yellow Gray Gray
Row 7: Yellow Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Yellow Gray Gray Yellow Gray Gray Gray Yellow Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Yellow Gray Gray Gray Yellow Gray Gray Gray Yellow Gray Gray Gray Gray Yellow Gray Gray Gray Gray Yellow Gray Gray Yellow
Row 10: Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray
Row 12: Gray Gray Gray Gray Yellow Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Yellow Gray Gray Gray Gray Gray
Row 14: Yellow Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray
Output:
Row 1: Yellow Pink Gray Gray Orange Yellow Pink Gray Gray Gray Red Orange Yellow Pink Gray Gray Gray Gray Gray Gray Gray Orange Yellow Pink
Row 2: Purple Gray Gray Gray Gray Purple Gray Gray Red Orange Yellow Pink Purple Gray Gray Red Gray Gray Red Gray Gray Red Purple Gray
Row 3: Gray Gray Red Gray Gray Gray Gray Orange Yellow Pink Purple Red Gray Gray Orange Yellow Pink Orange Yellow Pink Orange Yellow Pink Gray
Row 4: Gray Orange Yellow Pink Red Gray Gray Gray Purple Red Orange Yellow Pink Gray Gray Purple Gray Gray Purple Red Gray Purple Gray Red
Row 5: Gray Gray Purple Orange Yellow Pink Gray Gray Orange Yellow Pink Purple Gray Gray Gray Gray Red Gray Orange Yellow Pink Red Orange Yellow
Row 6: Red Gray Gray Gray Purple Gray Gray Gray Red Purple Gray Red Gray Gray Red Orange Yellow Pink Red Purple Orange Yellow Pink Purple
Row 7: Yellow Pink Gray Gray Gray Gray Gray Orange Yellow Pink Orange Yellow Pink Orange Yellow Pink Purple Orange Yellow Pink Gray Purple Gray Gray
Row 8: Purple Gray Red Gray Gray Gray Red Gray Purple Gray Red Purple Gray Gray Purple Red Gray Gray Purple Gray Red Gray Gray Red
Row 9: Red Orange Yellow Pink Gray Orange Yellow Pink Gray Orange Yellow Pink Gray Red Orange Yellow Pink Gray Red Orange Yellow Pink Orange Yellow
Row 10: Yellow Pink Purple Gray Gray Gray Purple Red Gray Gray Purple Gray Orange Yellow Pink Purple Gray Orange Yellow Pink Purple Red Gray Purple
Row 11: Purple Gray Gray Gray Red Gray Orange Yellow Pink Red Gray Gray Gray Purple Gray Gray Red Gray Purple Gray Orange Yellow Pink Gray
Row 12: Gray Gray Gray Orange Yellow Pink Gray Purple Orange Yellow Pink Gray Gray Gray Red Orange Yellow Pink Red Gray Gray Purple Gray Gray
Row 13: Red Gray Gray Gray Purple Gray Gray Red Gray Purple Gray Gray Gray Orange Yellow Pink Purple Orange Yellow Pink Gray Red Gray Gray
Row 14: Yellow Pink Gray Gray Gray Gray Orange Yellow Pink Gray Gray Gray Gray Red Purple Gray Gray Gray Purple Red Orange Yellow Pink Gray
Row 15: Purple Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Orange Yellow Pink Gray Gray Gray Orange Yellow Pink Purple Gray Gray
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Orange Yellow Pink Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Orange Yellow Pink Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Purple Blue Blue Blue Orange Yellow Pink Blue Blue Blue Blue Blue Blue
Row 7: Red Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue
Row 8: Yellow Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Purple Blue Red Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue
Row 10: Blue Orange Yellow Pink Blue Red Blue Blue Blue Orange Yellow Pink Blue Blue
Row 11: Blue Blue Purple Blue Orange Yellow Pink Blue Blue Blue Purple Blue Blue Red
Row 12: Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Orange Yellow
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
Example 3
Input:
Row 1: Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Black Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Black
Row 6: Black Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Red Blue Blue Blue Orange Black Pink Blue Blue Blue Red Blue Blue Red Blue Blue Red Orange Black Pink Blue Blue Blue Blue Blue Blue
Row 2: Orange Black Pink Blue Blue Blue Purple Blue Blue Blue Orange Black Pink Orange Black Pink Orange Black Pink Purple Red Blue Blue Blue Blue Blue Blue
Row 3: Blue Purple Blue Blue Blue Blue Blue Blue Red Blue Blue Purple Blue Blue Purple Blue Blue Purple Blue Orange Black Pink Blue Red Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Orange Black Pink Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Purple Blue Orange Black Pink Blue Red
Row 5: Red Blue Blue Blue Red Blue Blue Blue Purple Blue Blue Red Blue Blue Blue Blue Red Orange Black Pink Blue Blue Blue Purple Blue Orange Black
Row 6: Black Pink Blue Orange Black Pink Blue Blue Blue Blue Orange Black Pink Blue Blue Orange Black Pink Purple Blue Blue Blue Blue Blue Red Blue Purple
Row 7: Purple Blue Blue Blue Purple Blue Blue Blue Blue Red Blue Purple Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Orange Black Pink Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Orange Black Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Purple Blue Blue
Row 9: Blue Blue Blue Blue Red Blue Blue Blue Red Purple Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Orange Black Pink Blue Blue Blue Blue
Row 10: Blue Blue Blue Orange Black Pink Blue Orange Black Pink Blue Blue Orange Black Pink Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue
Row 4: Blue Blue Gray Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Gray Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue
Row 9: Gray Blue Blue Blue Blue Blue Gray Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Gray Blue Blue Blue Gray Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue
Row 14: Blue Blue Gray Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Gray Blue Blue Blue Gray Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Gray Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue
Row 19: Gray Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 21: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Gray Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Gray Blue Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Blue Blue Blue Red Blue Blue Blue Orange Gray Pink Blue Orange Gray Pink Blue Red Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue
Blue Blue Blue Orange Gray Pink Blue Blue Red Purple Blue Blue Blue Purple Blue Orange Gray Pink Blue Blue Orange Gray Pink Blue Red Blue Blue Blue
Blue Blue Red Blue Purple Red Blue Orange Gray Pink Blue Blue Blue Red Blue Blue Purple Blue Blue Red Blue Purple Blue Orange Gray Pink Blue Blue
Blue Orange Gray Pink Orange Gray Pink Blue Purple Red Blue Blue Orange Gray Pink Blue Blue Blue Orange Gray Pink Red Blue Blue Purple Blue Red Blue
Blue Blue Purple Blue Blue Purple Blue Blue Orange Gray Pink Blue Red Purple Blue Blue Blue Blue Blue Purple Orange Gray Pink Blue Blue Orange Gray Pink
Blue Blue Blue Red Blue Blue Blue Blue Blue Purple Blue Orange Gray Pink Red Blue Blue Blue Blue Red Blue Purple Blue Blue Blue Blue Purple Blue
Blue Blue Orange Gray Pink Blue Blue Blue Blue Blue Blue Blue Purple Orange Gray Pink Blue Blue Orange Gray Pink Red Blue Blue Blue Blue Blue Blue
Red Blue Blue Purple Blue Blue Red Blue Blue Red Blue Blue Blue Blue Purple Blue Blue Red Blue Purple Orange Gray Pink Blue Blue Blue Red Blue
Gray Pink Blue Blue Blue Orange Gray Pink Orange Gray Pink Blue Blue Red Blue Blue Orange Gray Pink Blue Blue Purple Red Blue Blue Orange Gray Pink
Purple Blue Blue Blue Blue Blue Purple Blue Blue Purple Blue Blue Orange Gray Pink Red Blue Purple Blue Blue Blue Orange Gray Pink Blue Blue Purple Blue
Blue Blue Blue Blue Red Blue Blue Blue Red Blue Blue Blue Red Purple Orange Gray Pink Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue
Red Blue Blue Orange Gray Pink Blue Orange Gray Pink Blue Orange Gray Pink Blue Purple Blue Red Blue Blue Blue Blue Blue Red Blue Blue Blue Blue
Gray Pink Red Blue Purple Blue Red Blue Purple Blue Blue Blue Purple Blue Blue Red Orange Gray Pink Blue Blue Red Orange Gray Pink Red Blue Blue
Purple Orange Gray Pink Blue Orange Gray Pink Blue Blue Blue Red Blue Blue Orange Gray Pink Purple Red Blue Orange Gray Pink Purple Orange Gray Pink Blue
Red Blue Purple Blue Blue Blue Purple Blue Blue Blue Orange Gray Pink Blue Red Purple Blue Orange Gray Pink Red Purple Blue Blue Blue Purple Blue Blue
Gray Pink Blue Blue Red Blue Blue Red Blue Blue Blue Purple Blue Orange Gray Pink Blue Blue Purple Orange Gray Pink Blue Blue Blue Blue Blue Blue
Purple Blue Red Orange Gray Pink Orange Gray Pink Blue Blue Blue Red Blue Purple Blue Blue Blue Blue Blue Purple Red Blue Blue Blue Blue Blue Blue
Red Orange Gray Pink Purple Red Blue Purple Blue Blue Blue Orange Gray Pink Blue Red Blue Blue Blue Blue Orange Gray Pink Blue Blue Blue Blue Blue
Gray Pink Purple Blue Orange Gray Pink Red Blue Blue Blue Blue Purple Blue Orange Gray Pink Red Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue
Purple Blue Blue Blue Blue Purple Orange Gray Pink Blue Blue Red Blue Blue Blue Purple Orange Gray Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue
Red Blue Blue Red Blue Blue Blue Purple Blue Blue Orange Gray Pink Blue Blue Blue Blue Purple Red Blue Blue Blue Blue Blue Blue Red Blue Blue
Gray Pink Orange Gray Pink Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Orange Gray Pink Blue Blue Blue Blue Orange Gray Pink Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Brown Yellow Brown Yellow Brown Yellow Yellow Brown Yellow Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Yellow Brown Yellow Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown
Row 9: Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Yellow Brown Brown Brown
Row 10: Brown Brown Brown Brown Yellow Brown Yellow Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Yellow Brown Yellow Brown Yellow Brown Brown Brown
Row 11: Brown Brown Brown Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Yellow Brown Brown Brown
Row 12: Brown Brown Brown Brown Yellow Brown Brown Yellow Brown Yellow Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown
Row 13: Brown Brown Brown Brown Yellow Yellow Brown Brown Yellow Yellow Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Yellow Brown Brown Yellow Yellow Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Brown Brown Yellow Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Yellow Yellow Yellow Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Blue Yellow Blue Yellow Blue Yellow Yellow Blue Yellow Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Yellow Blue Blue Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Blue Blue Blue Yellow Brown Brown Brown Brown Brown Brown Yellow Blue Yellow Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown
Row 9: Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Yellow Blue Blue Blue Yellow Brown Brown Brown
Row 10: Brown Brown Brown Brown Yellow Blue Yellow Blue Blue Yellow Brown Brown Brown Brown Brown Brown Brown Yellow Blue Yellow Blue Yellow Brown Brown Brown
Row 11: Brown Brown Brown Brown Yellow Yellow Yellow Blue Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Yellow Blue Blue Blue Yellow Brown Brown Brown
Row 12: Brown Brown Brown Brown Yellow Blue Blue Yellow Blue Yellow Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown
Row 13: Brown Brown Brown Brown Yellow Yellow Blue Blue Yellow Yellow Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Yellow Brown Brown Yellow Yellow Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Brown Brown Yellow Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Yellow Yellow Yellow Brown Brown Brown
Example 2
Input:
Row 1: Purple Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Purple Gray Gray Purple Gray Gray Gray Purple Purple Purple Purple Purple Purple Gray Gray
Row 3: Purple Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray
Row 4: Purple Gray Gray Purple Gray Gray Gray Purple Purple Gray Gray Gray Purple Gray Gray
Row 5: Purple Gray Gray Purple Gray Gray Gray Purple Purple Gray Gray Gray Purple Gray Gray
Row 6: Purple Purple Purple Purple Gray Gray Gray Purple Purple Purple Purple Purple Purple Gray Purple
Row 7: Gray Gray Gray Purple Gray Gray Gray Purple Purple Gray Gray Purple Purple Gray Purple
Row 8: Gray Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Purple Purple Gray Purple
Row 9: Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple
Row 12: Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Gray Purple Gray Gray
Row 13: Gray Gray Purple Purple Purple Gray Gray Gray Gray Gray Purple Gray Purple Purple Purple
Row 14: Gray Gray Purple Purple Purple Gray Gray Gray Gray Gray Purple Gray Gray Gray Purple
Row 15: Gray Gray Purple Purple Purple Purple Gray Gray Gray Gray Purple Gray Gray Purple Purple
Row 16: Gray Gray Gray Gray Purple Gray Purple Gray Purple Gray Purple Gray Gray Purple Purple
Row 17: Gray Gray Gray Gray Purple Gray Gray Purple Gray Gray Purple Gray Gray Purple Purple
Output:
Row 1: Purple Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Purple Gray Gray Purple Gray Gray Gray Purple Purple Purple Purple Purple Purple Gray Gray
Row 3: Purple Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray
Row 4: Purple Gray Gray Purple Blue Blue Blue Purple Purple Blue Blue Blue Purple Gray Gray
Row 5: Purple Gray Gray Purple Blue Blue Blue Purple Purple Blue Blue Blue Purple Gray Gray
Row 6: Purple Purple Purple Purple Blue Blue Blue Purple Purple Purple Purple Purple Purple Gray Purple
Row 7: Gray Gray Gray Purple Blue Blue Blue Purple Purple Blue Blue Purple Purple Gray Purple
Row 8: Gray Gray Gray Purple Purple Purple Purple Purple Blue Blue Blue Purple Purple Gray Purple
Row 9: Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple
Row 12: Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Gray Purple Gray Gray
Row 13: Gray Gray Purple Purple Purple Gray Gray Gray Gray Gray Purple Gray Purple Purple Purple
Row 14: Gray Gray Purple Purple Purple Gray Gray Gray Gray Gray Purple Gray Gray Gray Purple
Row 15: Gray Gray Purple Purple Purple Purple Gray Gray Gray Gray Purple Gray Gray Purple Purple
Row 16: Gray Gray Gray Gray Purple Gray Purple Gray Purple Gray Purple Gray Gray Purple Purple
Row 17: Gray Gray Gray Gray Purple Gray Gray Purple Gray Gray Purple Gray Gray Purple Purple
Example 3
Input:
Row 1: Green Green Green Gray Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Green Gray Gray Green
Row 2: Green Green Green Gray Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Green Gray Green Green
Row 3: Green Green Green Gray Green Green Green Green Gray Green Green Gray Gray Gray Gray Gray Gray Green Green Green Gray Gray Gray
Row 4: Green Green Green Gray Green Green Green Green Gray Green Green Gray Green Gray Gray Green Gray Green Green Green Green Green Gray
Row 5: Green Green Green Gray Gray Gray Gray Gray Gray Green Green Gray Green Green Green Green Gray Green Green Green Green Green Gray
Row 6: Green Green Green Green Gray Green Gray Gray Green Green Green Gray Gray Gray Gray Gray Gray Green Green Green Green Green Gray
Row 7: Green Green Green Green Gray Gray Gray Gray Gray Gray Gray Green Green Green Green Green Gray Gray Gray Gray Gray Gray Gray
Row 8: Green Green Green Green Green Green Gray Green Green Gray Gray Green Green Green Green Green Gray Green Green Green Green Green Gray
Row 9: Green Green Green Green Green Green Gray Green Green Green Gray Green Green Green Green Green Gray Gray Gray Gray Gray Gray Gray
Row 10: Green Green Green Green Green Green Gray Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Gray Gray Gray Gray Gray Gray Gray Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Gray Green Green Green Gray Gray Green Green Green Gray Green Green Green Green Gray Gray Gray Gray Gray Gray Gray Green
Row 13: Gray Green Green Green Gray Gray Gray Gray Gray Gray Gray Green Green Green Green Gray Green Green Green Gray Gray Gray Green
Row 14: Green Gray Gray Green Green Gray Green Gray Gray Green Gray Green Green Green Green Gray Gray Gray Gray Gray Gray Gray Green
Row 15: Gray Gray Green Green Green Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Green Green Green
Output:
Row 1: Green Green Green Gray Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Green Gray Gray Green
Row 2: Green Green Green Gray Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Green Gray Green Green
Row 3: Green Green Green Gray Green Green Green Green Gray Green Green Gray Gray Gray Gray Gray Gray Green Green Green Gray Gray Gray
Row 4: Green Green Green Gray Green Green Green Green Gray Green Green Gray Blue Gray Gray Blue Gray Green Green Green Green Green Gray
Row 5: Green Green Green Gray Gray Gray Gray Gray Gray Green Green Gray Blue Blue Blue Blue Gray Green Green Green Green Green Gray
Row 6: Green Green Green Green Gray Blue Gray Gray Green Green Green Gray Gray Gray Gray Gray Gray Green Green Green Green Green Gray
Row 7: Green Green Green Green Gray Gray Gray Gray Gray Gray Gray Green Green Green Green Green Gray Gray Gray Gray Gray Gray Gray
Row 8: Green Green Green Green Green Green Gray Blue Blue Gray Gray Green Green Green Green Green Gray Blue Blue Blue Blue Blue Gray
Row 9: Green Green Green Green Green Green Gray Blue Blue Blue Gray Green Green Green Green Green Gray Gray Gray Gray Gray Gray Gray
Row 10: Green Green Green Green Green Green Gray Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Gray Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Gray Green Green Green Gray Gray Blue Blue Blue Gray Green Green Green Green Gray Gray Gray Gray Gray Gray Gray Green
Row 13: Gray Green Green Green Gray Gray Gray Gray Gray Gray Gray Green Green Green Green Gray Blue Blue Blue Gray Gray Gray Green
Row 14: Green Gray Gray Green Green Gray Green Gray Gray Blue Gray Green Green Green Green Gray Gray Gray Gray Gray Gray Gray Green
Row 15: Gray Gray Green Green Green Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Orange Gray Orange Gray Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange
Row 3: Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange Gray Gray Gray Gray Gray
Row 4: Orange Orange Gray Orange Orange Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Gray Orange Orange Gray Orange Orange Orange Orange
Row 5: Orange Gray Orange Orange Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange Gray Gray Gray Orange Orange
Row 6: Orange Gray Orange Gray Orange Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange
Row 7: Orange Orange Orange Orange Gray Gray Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange
Row 8: Orange Orange Gray Gray Orange Gray Orange Orange Orange Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Gray Gray
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Gray Gray
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Gray Gray
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Gray Gray Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Gray
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Gray Orange Gray Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange
Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Gray Blue Blue Blue Gray Blue Blue Gray Gray Gray Gray Gray
Orange Orange Gray Orange Orange Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Gray Blue Blue Gray Orange Orange Orange Orange
Orange Gray Orange Orange Orange Gray Orange Gray Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Gray Blue Blue Gray Gray Gray Orange Orange
Orange Gray Orange Gray Orange Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange
Orange Orange Orange Orange Gray Gray Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange
Orange Orange Gray Gray Blue Gray Orange Orange Orange Orange Gray Blue Gray Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Gray Blue Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Blue Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Blue Gray Gray
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Blue Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Blue Gray Gray
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Blue Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Blue Gray Gray
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Blue Blue Blue Gray Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Blue Gray Gray Blue Blue Blue Gray Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray
Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Gray
Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 24: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 25: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 26: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 27: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray
Row 24: Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray
Row 25: Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray
Row 26: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange
Row 27: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Green Green Green Green Pink Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Green Green Green Green Pink Pink Pink Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Green Green Pink Green Pink Pink Pink Green Pink Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Green Green Green Pink Green Pink Green Pink Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Green Pink Pink Green Pink Pink Pink Green Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Green Pink Pink Green Pink Pink Pink Green Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Green Green Green Pink Green Pink Green Pink Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Green Green Pink Green Pink Pink Pink Green Pink Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Green Green Green Green Pink Pink Pink Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Green Green Green Green Pink Green Green Green Green Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 27: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 28: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Green Green Green Green Pink Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Green Green Green Green Pink Pink Pink Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Green Green Pink Green Pink Pink Pink Green Pink Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Green Green Green Pink Green Pink Green Pink Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Green Pink Pink Green Pink Pink Pink Green Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Green Pink Pink Green Pink Pink Pink Green Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Green Green Green Pink Green Pink Green Pink Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Green Green Pink Green Pink Pink Pink Green Pink Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Green Green Green Green Pink Pink Pink Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Green Green Green Green Pink Green Green Green Green Pink Red Red Red Red Pink Red Red Red Red Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Pink Pink Pink Red Red Red Red Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Pink Red Pink Pink Pink Red Pink Red Red Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Pink Red Pink Red Pink Red Red Red Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Red Pink Pink Pink Red Pink Pink Red Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Red Pink Pink Pink Red Pink Pink Red Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Pink Red Pink Red Pink Red Red Red Pink Pink
Row 25: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Pink Red Pink Pink Pink Red Pink Red Red Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Pink Pink Pink Red Red Red Red Pink Pink
Row 27: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Pink Red Red Red Red Pink Red Red
Row 28: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red
Example 3
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Red Red Red Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Red Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Red Red Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Red Red Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Red Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Red Red Red Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Red Red Red Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Red Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Red Red Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Red Red Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Red Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Red Red Red Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Black Yellow Black Black Black Black Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Black Yellow Black Black Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Black Yellow Yellow Black Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Black Black Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Black Black Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Black Yellow Yellow Black Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Black Yellow Black Black Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Black Yellow Black Black Black Black Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Here is the input grid for the test example:
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Green Red Green Green Green Red Green Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Green Red Green Green Green Red Green Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 21: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 22: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Green Red Green Green Green Red Green Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Green Red Green Green Green Red Green Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Blue Red Blue Blue Blue Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Blue Red Blue Blue Blue Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange Brown Red Brown Orange Red Brown Orange Orange Orange Red Brown Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Red Brown Red Orange Brown Red Orange Orange Orange Brown Red Orange
Output:
Row 1: Orange Orange Brown Red Brown Orange Red Brown Orange Orange Orange Red Brown Orange
Row 2: Orange Orange Brown Red Brown Orange Red Brown Orange Orange Orange Red Brown Orange
Row 3: Orange Orange Brown Red Brown Orange Red Brown Orange Orange Orange Red Brown Orange
Row 4: Orange Orange Brown Red Brown Orange Red Brown Orange Orange Orange Red Brown Orange
Row 5: Orange Orange Brown Red Brown Orange Red Brown Orange Orange Orange Red Brown Orange
Row 6: Orange Orange Brown Red Brown Orange Red Brown Orange Orange Orange Red Brown Orange
Row 7: Orange Orange Brown Red Brown Orange Red Brown Orange Orange Orange Red Brown Orange
Row 8: Orange Orange Brown Red Brown Orange Red Brown Orange Orange Orange Red Brown Orange
Row 9: Orange Orange Brown Red Brown Orange Red Brown Orange Orange Orange Red Brown Orange
Row 10: Orange Orange Brown Red Brown Orange Red Brown Orange Orange Orange Red Brown Orange
Row 11: Orange Orange Brown Red Brown Orange Red Brown Orange Orange Orange Red Brown Orange
Row 12: Orange Orange Brown Red Brown Orange Red Brown Orange Orange Orange Red Brown Orange
Row 13: Orange Orange Gray Gray Gray Orange Gray Gray Orange Orange Orange Gray Gray Orange
Row 14: Orange Orange Red Brown Red Orange Brown Red Orange Orange Orange Brown Red Orange
Row 15: Orange Orange Red Brown Red Orange Brown Red Orange Orange Orange Brown Red Orange
Row 16: Orange Orange Red Brown Red Orange Brown Red Orange Orange Orange Brown Red Orange
Row 17: Orange Orange Red Brown Red Orange Brown Red Orange Orange Orange Brown Red Orange
Row 18: Orange Orange Red Brown Red Orange Brown Red Orange Orange Orange Brown Red Orange
Row 19: Orange Orange Red Brown Red Orange Brown Red Orange Orange Orange Brown Red Orange
Row 20: Orange Orange Red Brown Red Orange Brown Red Orange Orange Orange Brown Red Orange
Row 21: Orange Orange Red Brown Red Orange Brown Red Orange Orange Orange Brown Red Orange
Row 22: Orange Orange Red Brown Red Orange Brown Red Orange Orange Orange Brown Red Orange
Row 23: Orange Orange Red Brown Red Orange Brown Red Orange Orange Orange Brown Red Orange
Row 24: Orange Orange Red Brown Red Orange Brown Red Orange Orange Orange Brown Red Orange
Row 25: Orange Orange Red Brown Red Orange Brown Red Orange Orange Orange Brown Red Orange
Example 2
Input:
Row 1: Pink Purple Purple Purple Purple Purple Orange
Row 2: Purple Purple Purple Purple Purple Purple Purple
Row 3: Brown Purple Purple Purple Purple Purple Black
Row 4: Purple Purple Purple Purple Purple Purple Purple
Row 5: Orange Purple Purple Purple Purple Purple Orange
Row 6: Blue Purple Purple Purple Purple Purple Blue
Row 7: Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple
Row 13: Brown Purple Purple Purple Purple Purple Green
Row 14: Purple Purple Purple Purple Purple Purple Purple
Row 15: Orange Purple Purple Purple Purple Purple Red
Row 16: Black Purple Purple Purple Purple Purple Green
Row 17: Purple Purple Purple Purple Purple Purple Purple
Row 18: Brown Purple Purple Purple Purple Purple Orange
Row 19: Red Purple Purple Purple Purple Purple Red
Row 20: Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Pink Pink Pink Gray Orange Orange Orange
Row 2: Purple Purple Purple Purple Purple Purple Purple
Row 3: Brown Brown Brown Gray Black Black Black
Row 4: Purple Purple Purple Purple Purple Purple Purple
Row 5: Orange Orange Orange Gray Orange Orange Orange
Row 6: Blue Blue Blue Gray Blue Blue Blue
Row 7: Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple
Row 13: Brown Brown Brown Gray Green Green Green
Row 14: Purple Purple Purple Purple Purple Purple Purple
Row 15: Orange Orange Orange Gray Red Red Red
Row 16: Black Black Black Gray Green Green Green
Row 17: Purple Purple Purple Purple Purple Purple Purple
Row 18: Brown Brown Brown Gray Orange Orange Orange
Row 19: Red Red Red Gray Red Red Red
Row 20: Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red
Row 2: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black
Row 6: Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple
Row 12: Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black
Row 13: Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black
Row 17: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink
Row 22: Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green
Row 23: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink
Row 26: Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black
Output:
Row 1: Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red
Row 2: Purple Purple Purple Purple Purple Purple Purple Gray Pink Pink Pink Pink Pink Pink Pink
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Green Green Green Green Green Green Green Gray Black Black Black Black Black Black Black
Row 6: Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple
Row 12: Red Red Red Red Red Red Red Gray Black Black Black Black Black Black Black
Row 13: Pink Pink Pink Pink Pink Pink Pink Gray Green Green Green Green Green Green Green
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black
Row 17: Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Green Green Green Green Green Green Green Gray Pink Pink Pink Pink Pink Pink Pink
Row 22: Red Red Red Red Red Red Red Gray Green Green Green Green Green Green Green
Row 23: Purple Purple Purple Purple Purple Purple Purple Gray Black Black Black Black Black Black Black
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Pink Pink
Row 26: Green Green Green Green Green Green Green Gray Black Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple
Row 2: Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red
Row 3: Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black
Row 4: Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red
Row 5: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple
Row 6: Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple
Row 11: Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red
Row 12: Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple
Row 15: Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black
Row 16: Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple
Row 20: Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red
Row 21: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red
Row 25: Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 28: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Red Red Red Red Red Red Gray Purple Purple Purple Purple Purple Purple Purple
Black Black Black Black Black Black Black Gray Red Red Red Red Red Red Red
Purple Purple Purple Purple Purple Purple Purple Gray Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Gray Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Gray Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Gray Black Black Black Black Black Black Black
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Black Black Black Black Black Black Black Gray Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Gray Red Red Red Red Red Red Red
Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple
Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black
Purple Purple Purple Purple Purple Purple Purple Gray Red Red Red Red Red Red Red
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Red Red Red Red Red Red Red Gray Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Gray Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Gray Black Black Black Black Black Black Black
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Purple Purple Purple Purple Purple Purple Purple Gray Red Red Red Red Red Red Red
Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Green Brown Brown Brown Brown Brown Green Pink Brown Brown Brown Brown Brown Brown Brown
Row 16: Green Brown Brown Brown Brown Brown Green Pink Brown Brown Brown Brown Brown Brown Brown
Row 17: Green Brown Brown Brown Brown Brown Green Pink Brown Brown Brown Brown Brown Brown Brown
Row 18: Green Brown Brown Brown Brown Brown Green Pink Brown Brown Brown Brown Brown Brown Brown
Row 19: Green Brown Brown Brown Brown Brown Green Pink Brown Brown Brown Brown Brown Brown Brown
Row 20: Green Brown Brown Brown Brown Brown Green Pink Brown Brown Brown Brown Brown Brown Brown
Row 21: Green Brown Brown Brown Brown Brown Green Pink Brown Brown Brown Brown Brown Brown Brown
Row 22: Green Brown Brown Brown Brown Brown Green Pink Brown Brown Brown Brown Brown Brown Brown
Row 23: Green Brown Brown Brown Brown Brown Green Pink Red Brown Brown Brown Brown Brown Brown
Row 24: Green Brown Brown Brown Brown Brown Green Pink Red Brown Brown Brown Brown Brown Brown
Row 25: Green Brown Brown Brown Brown Brown Green Pink Red Brown Brown Brown Brown Brown Brown
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 21: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Black Blue Red Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Black Blue Red Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Black Blue Red Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Red Blue Blue Blue Blue Blue Brown Blue Blue
Row 15: Blue Blue Blue Blue Blue Black Blue Red Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Red Blue Blue Blue Blue Blue Brown Blue Blue
Row 16: Blue Blue Blue Blue Blue Black Blue Red Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Red Blue Blue Blue Blue Blue Brown Blue Blue
Row 17: Blue Blue Blue Blue Blue Black Blue Red Purple Blue Blue Blue Blue Blue Blue Black Blue Blue Red Blue Blue Blue Blue Blue Brown Blue Blue
Row 18: Blue Blue Blue Blue Blue Black Blue Red Purple Blue Blue Blue Blue Blue Blue Black Blue Blue Red Blue Blue Blue Blue Blue Brown Blue Blue
Row 19: Blue Blue Blue Blue Blue Black Blue Red Purple Blue Blue Blue Blue Blue Blue Black Blue Blue Red Blue Blue Blue Blue Blue Brown Blue Blue
Row 20: Blue Blue Blue Blue Blue Black Blue Red Purple Blue Blue Blue Blue Blue Blue Black Blue Blue Red Blue Blue Blue Blue Blue Brown Blue Blue
Row 21: Blue Blue Blue Blue Blue Black Blue Red Purple Blue Blue Blue Blue Blue Blue Black Blue Blue Red Blue Blue Blue Blue Blue Brown Blue Blue
Row 22: Blue Blue Blue Blue Blue Black Blue Red Purple Blue Blue Blue Blue Blue Blue Black Blue Blue Red Blue Blue Blue Blue Blue Brown Blue Blue
Row 23: Blue Blue Blue Blue Blue Black Blue Red Purple Blue Blue Blue Blue Blue Blue Black Blue Blue Red Blue Blue Blue Blue Blue Brown Blue Blue
Row 24: Blue Blue Blue Blue Blue Black Blue Red Purple Blue Blue Blue Blue Blue Blue Black Blue Blue Red Blue Blue Blue Blue Blue Brown Blue Blue
Row 25: Blue Blue Blue Blue Blue Black Blue Red Purple Blue Blue Blue Blue Blue Blue Black Blue Red Red Blue Blue Blue Blue Blue Brown Blue Blue
Example 3
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Red Black Black Black Black Black Black Orange Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Yellow Black Black Black Black Red Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Blue Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Blue Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Blue Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Blue Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green
Row 8: Black Black Black Black Blue Black Blue Black Black Black Black Black Black Red Black Black Black Black Black Black Orange Black Green
Row 9: Black Black Black Black Blue Black Blue Black Black Black Black Black Black Red Black Black Black Black Black Black Orange Black Green
Row 10: Black Black Black Red Blue Black Blue Black Black Black Black Black Black Red Black Black Black Black Black Black Orange Black Green
Row 11: Black Black Black Red Blue Black Blue Black Black Black Black Black Black Red Black Black Black Black Black Black Orange Black Green
Row 12: Black Black Black Red Blue Black Blue Black Black Black Black Black Black Red Black Black Black Black Black Black Orange Black Green
Row 13: Black Black Black Red Blue Black Blue Black Black Black Black Black Black Red Black Black Black Black Black Black Orange Black Green
Row 14: Black Black Black Red Blue Black Blue Black Black Black Black Black Black Red Black Black Black Pink Black Black Orange Black Green
Row 15: Black Black Black Red Blue Black Blue Black Black Yellow Black Black Black Red Red Black Black Pink Black Black Orange Black Green
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Purple Pink Pink Orange Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Black Pink Pink Purple Pink Pink Orange Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Brown Pink Pink Blue Black Pink Pink Purple Pink Pink Orange Pink Pink Pink Purple Pink
Pink Pink Pink Pink Pink Pink Brown Pink Pink Blue Black Pink Pink Purple Pink Pink Orange Pink Pink Pink Purple Black
Pink Pink Pink Pink Pink Pink Brown Pink Pink Blue Black Pink Pink Purple Pink Pink Orange Pink Pink Pink Purple Black
Pink Pink Pink Pink Pink Pink Brown Pink Pink Blue Black Pink Pink Purple Pink Pink Orange Pink Pink Pink Purple Black
Pink Pink Pink Pink Pink Pink Brown Pink Pink Blue Black Pink Pink Purple Pink Pink Orange Pink Pink Pink Purple Black
Pink Pink Pink Pink Orange Pink Brown Pink Pink Blue Black Pink Pink Purple Pink Pink Orange Pink Pink Pink Purple Black
Pink Pink Pink Yellow Orange Pink Brown Pink Pink Blue Black Pink Pink Purple Pink Pink Orange Pink Pink Pink Purple Black
Pink Pink Pink Yellow Orange Pink Brown Pink Pink Blue Black Pink Pink Purple Pink Pink Orange Pink Pink Pink Purple Black
Pink Pink Pink Yellow Orange Pink Brown Pink Pink Blue Black Pink Pink Purple Pink Pink Orange Pink Pink Pink Purple Black
Pink Pink Pink Yellow Orange Pink Brown Pink Pink Blue Black Pink Pink Purple Pink Pink Orange Pink Pink Pink Purple Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Purple Purple Purple Black Black Black Black Black Black Purple Purple Purple Purple Black Purple Black Black Black Black Purple Black Purple Black Purple Black
Row 2: Purple Black Black Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Purple Purple Black Black Black Black Purple Black Black Black
Row 3: Black Black Black Black Black Purple Purple Black Purple Purple Purple Black Purple Purple Purple Black Black Black Purple Black Purple Black Black Purple Purple Black Black
Row 4: Black Black Black Black Black Black Black Purple Black Black Black Purple Black Black Purple Black Black Black Black Black Black Purple Black Purple Black Black Purple
Row 5: Black Black Purple Black Black Black Purple Black Purple Black Purple Purple Purple Black Black Purple Black Purple Purple Purple Black Purple Purple Black Black Black Purple
Row 6: Black Black Black Black Black Black Black Black Black Purple Black Black Black Black Black Black Black Black Black Black Purple Black Black Black Black Black Black
Row 7: Black Purple Purple Purple Black Black Black Purple Black Black Purple Black Black Black Black Black Black Black Purple Black Black Purple Black Black Black Black Purple
Row 8: Black Black Black Purple Black Black Black Black Purple Black Purple Black Black Black Purple Black Black Black Black Black Black Purple Black Black Black Purple Purple
Row 9: Black Purple Black Black Black Purple Black Black Black Black Purple Black Purple Black Purple Black Black Black Black Black Black Purple Black Black Black Purple Black
Row 10: Purple Purple Black Purple Black Black Purple Black Purple Black Black Black Black Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 11: Black Black Purple Purple Black Black Purple Purple Black Purple Black Black Black Purple Black Black Black Black Black Black Purple Black Purple Black Black Black Black
Row 12: Purple Black Black Black Red Purple Black Purple Black Purple Black Black Purple Black Purple Black Green Purple Black Purple Black Purple Purple Black Purple Purple Purple
Row 13: Black Purple Purple Purple Red Purple Purple Purple Black Black Black Black Black Purple Purple Purple Green Purple Black Black Black Black Black Purple Black Purple Black
Row 14: Purple Purple Black Purple Purple Black Black Black Purple Purple Purple Purple Purple Black Black Black Purple Black Black Purple Purple Black Purple Purple Black Black Purple
Row 15: Purple Black Black Black Purple Black Black Black Black Black Black Purple Purple Purple Purple Black Purple Black Black Purple Purple Black Purple Purple Black Black Purple
Row 16: Purple Purple Purple Purple Black Black Purple Black Black Black Black Black Purple Purple Black Black Black Black Black Black Black Black Black Purple Black Purple Purple
Row 17: Black Purple Purple Black Purple Black Purple Purple Black Black Purple Black Black Purple Black Purple Black Purple Purple Purple Black Black Black Black Black Purple Black
Row 18: Black Black Black Black Black Black Purple Black Purple Black Purple Black Purple Black Black Purple Purple Purple Purple Purple Black Black Black Black Black Purple Black
Output:
Row 1: Black Black Purple Purple Purple Black Black Black Black Black Black Purple Purple Purple Purple Black Purple Black Black Black Black Purple Black Purple Black Purple Black
Row 2: Purple Black Black Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Purple Black Black Black Black Purple Black Black Black
Row 3: Black Black Black Black Green Purple Purple Black Purple Purple Purple Black Purple Purple Purple Black Green Black Purple Black Purple Black Black Purple Purple Black Black
Row 4: Black Black Black Black Green Black Black Purple Black Black Black Purple Black Black Purple Black Green Black Black Black Black Purple Black Purple Black Black Purple
Row 5: Black Black Purple Black Green Black Purple Black Purple Black Purple Purple Purple Black Black Purple Green Purple Purple Purple Black Purple Purple Black Black Black Purple
Row 6: Black Black Black Black Green Black Black Black Black Purple Black Black Black Black Black Black Green Black Black Black Purple Black Black Black Black Black Black
Row 7: Black Purple Purple Purple Green Black Black Purple Black Black Purple Black Black Black Black Black Green Black Purple Black Black Purple Black Black Black Black Purple
Row 8: Black Black Black Purple Green Black Black Black Purple Black Purple Black Black Black Purple Black Green Black Black Black Black Purple Black Black Black Purple Purple
Row 9: Black Purple Black Black Green Purple Black Black Black Black Purple Black Purple Black Purple Black Green Black Black Black Black Purple Black Black Black Purple Black
Row 10: Purple Purple Black Purple Green Black Purple Black Purple Black Black Black Black Black Black Black Green Purple Black Black Black Black Purple Black Black Black Black
Row 11: Black Black Purple Purple Green Black Purple Purple Black Purple Black Black Black Purple Black Black Green Black Black Black Purple Black Purple Black Black Black Black
Row 12: Purple Black Black Black Red Purple Black Purple Black Purple Black Black Purple Black Purple Black Green Purple Black Purple Black Purple Purple Black Purple Purple Purple
Row 13: Black Purple Purple Purple Red Purple Purple Purple Black Black Black Black Black Purple Purple Purple Green Purple Black Black Black Black Black Purple Black Purple Black
Row 14: Purple Purple Black Purple Purple Black Black Black Purple Purple Purple Purple Purple Black Black Black Purple Black Black Purple Purple Black Purple Purple Black Black Purple
Row 15: Purple Black Black Black Purple Black Black Black Black Black Black Purple Purple Purple Purple Black Purple Black Black Purple Purple Black Purple Purple Black Black Purple
Row 16: Purple Purple Purple Purple Black Black Purple Black Black Black Black Black Purple Purple Black Black Black Black Black Black Black Black Black Purple Black Purple Purple
Row 17: Black Purple Purple Black Purple Black Purple Purple Black Black Purple Black Black Purple Black Purple Black Purple Purple Purple Black Black Black Black Black Purple Black
Row 18: Black Black Black Black Black Black Purple Black Purple Black Purple Black Purple Black Black Purple Purple Purple Purple Purple Black Black Black Black Black Purple Black
Example 2
Input:
Row 1: Yellow Black Black Black Black Black Yellow Yellow Yellow Yellow Black Black Black Black Black Yellow Yellow
Row 2: Black Green Black Black Black Black Black Black Black Black Yellow Black Black Black Red Yellow Black
Row 3: Black Green Black Black Yellow Black Black Yellow Black Black Black Yellow Black Black Red Yellow Yellow
Row 4: Yellow Black Black Black Black Black Yellow Yellow Yellow Black Black Black Black Black Black Black Black
Row 5: Yellow Black Yellow Black Black Black Yellow Yellow Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Yellow Yellow Black Black Yellow
Row 7: Black Black Black Yellow Black Black Black Yellow Black Black Black Black Yellow Black Black Black Yellow
Row 8: Black Black Black Yellow Yellow Black Yellow Black Black Yellow Black Yellow Yellow Yellow Black Black Black
Row 9: Black Black Yellow Yellow Black Black Black Black Black Yellow Yellow Black Black Yellow Black Black Black
Row 10: Black Black Black Black Black Black Yellow Black Black Black Yellow Yellow Yellow Black Black Black Yellow
Row 11: Yellow Black Yellow Black Black Black Yellow Yellow Black Black Black Black Black Black Black Black Yellow
Row 12: Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black Yellow Black
Row 13: Black Yellow Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Yellow Yellow Yellow Black Black Black Black Black Black Black Black Black Black Yellow Black Yellow Yellow
Row 15: Yellow Yellow Yellow Black Yellow Black Yellow Yellow Yellow Black Black Black Yellow Black Black Black Black
Output:
Row 1: Yellow Black Black Black Black Black Yellow Yellow Yellow Yellow Black Black Black Black Black Yellow Yellow
Row 2: Black Green Black Black Black Black Black Black Black Black Yellow Black Black Black Red Yellow Black
Row 3: Black Green Black Black Yellow Black Black Yellow Black Black Black Yellow Black Black Red Yellow Yellow
Row 4: Yellow Green Black Black Black Black Yellow Yellow Yellow Black Black Black Black Black Green Black Black
Row 5: Yellow Green Yellow Black Black Black Yellow Yellow Black Black Black Black Black Black Green Black Black
Row 6: Black Green Black Black Black Black Black Black Black Black Black Black Yellow Yellow Green Black Yellow
Row 7: Black Green Black Yellow Black Black Black Yellow Black Black Black Black Yellow Black Green Black Yellow
Row 8: Black Green Black Yellow Yellow Black Yellow Black Black Yellow Black Yellow Yellow Yellow Green Black Black
Row 9: Black Green Yellow Yellow Black Black Black Black Black Yellow Yellow Black Black Yellow Green Black Black
Row 10: Black Green Black Black Black Black Yellow Black Black Black Yellow Yellow Yellow Black Green Black Yellow
Row 11: Yellow Green Yellow Black Black Black Yellow Yellow Black Black Black Black Black Black Green Black Yellow
Row 12: Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Black
Row 13: Black Yellow Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Yellow Yellow Yellow Black Black Black Black Black Black Black Black Black Black Yellow Black Yellow Yellow
Row 15: Yellow Yellow Yellow Black Yellow Black Yellow Yellow Yellow Black Black Black Yellow Black Black Black Black
Example 3
Input:
Row 1: Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple
Row 2: Purple Orange Purple Purple Purple Purple Orange Orange Purple Orange Purple Purple Purple Purple Orange Purple Orange Orange
Row 3: Orange Purple Purple Orange Purple Purple Orange Orange Orange Orange Purple Purple Orange Purple Purple Purple Purple Purple
Row 4: Purple Purple Red Purple Orange Orange Orange Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple
Row 5: Purple Purple Red Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Orange Purple Orange
Row 6: Purple Purple Purple Purple Orange Orange Purple Orange Purple Orange Purple Orange Orange Purple Purple Purple Orange Orange
Row 7: Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Orange Purple Purple Purple Purple Purple Orange Orange Purple Purple Orange Purple Purple Orange Purple Purple Green Purple
Row 9: Orange Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Orange Green Orange
Row 10: Purple Orange Orange Orange Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Orange Orange Orange Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Row 12: Purple Purple Purple Orange Purple Purple Purple Purple Purple Orange Purple Orange Orange Purple Purple Purple Orange Purple
Output:
Row 1: Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple
Row 2: Purple Orange Purple Purple Purple Purple Orange Orange Purple Orange Purple Purple Purple Purple Orange Purple Orange Orange
Row 3: Orange Purple Purple Orange Purple Purple Orange Orange Orange Orange Purple Purple Orange Purple Purple Purple Purple Purple
Row 4: Purple Purple Red Purple Orange Orange Orange Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple
Row 5: Purple Purple Red Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Orange Purple Orange
Row 6: Purple Purple Green Purple Orange Orange Purple Orange Purple Orange Purple Orange Orange Purple Purple Purple Orange Orange
Row 7: Purple Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 8: Orange Purple Purple Purple Purple Purple Orange Orange Purple Purple Orange Purple Purple Orange Purple Purple Green Purple
Row 9: Orange Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Orange Green Orange
Row 10: Purple Orange Orange Orange Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Orange Orange Orange Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Row 12: Purple Purple Purple Orange Purple Purple Purple Purple Purple Orange Purple Orange Orange Purple Purple Purple Orange Purple
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Blue Brown Blue Blue Blue Blue Blue Brown Blue Blue Brown Blue Brown Brown Brown Brown Brown Blue
Row 2: Blue Blue Red Brown Brown Blue Blue Blue Blue Blue Brown Blue Blue Brown Blue Blue Blue Blue Brown Blue
Row 3: Blue Blue Red Blue Blue Brown Brown Blue Blue Brown Brown Brown Blue Brown Brown Blue Brown Blue Blue Brown
Row 4: Blue Brown Blue Brown Blue Blue Blue Brown Blue Brown Brown Blue Blue Blue Blue Brown Blue Brown Blue Brown
Row 5: Brown Brown Blue Blue Blue Brown Blue Brown Blue Blue Brown Brown Brown Blue Brown Brown Brown Brown Blue Blue
Row 6: Blue Brown Blue Blue Blue Brown Brown Brown Blue Brown Blue Blue Blue Blue Brown Blue Brown Brown Brown Brown
Row 7: Brown Brown Blue Blue Blue Blue Blue Brown Brown Blue Brown Blue Blue Blue Brown Blue Brown Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Brown Blue Brown Brown Brown Brown Brown Brown Blue Blue Blue Brown Blue Brown
Row 9: Blue Blue Blue Brown Brown Blue Blue Brown Blue Brown Brown Blue Blue Blue Brown Brown Brown Blue Blue Brown
Row 10: Blue Blue Blue Blue Brown Blue Brown Brown Brown Brown Blue Blue Blue Brown Brown Blue Brown Brown Brown Brown
Row 11: Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Brown Blue Brown Brown Blue Blue Brown Brown Blue Brown Blue Blue Brown Brown Blue Blue Blue Blue
Row 13: Brown Blue Brown Blue Blue Blue Brown Blue Brown Blue Brown Blue Blue Brown Brown Blue Brown Blue Blue Brown
Row 14: Brown Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue
Row 15: Brown Blue Brown Brown Blue Brown Blue Brown Blue Blue Brown Brown Blue Brown Blue Blue Blue Blue Green Blue
Row 16: Brown Brown Blue Blue Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Green Blue
Row 17: Blue Blue Brown Blue Blue Brown Brown Brown Blue Brown Blue Brown Blue Brown Blue Blue Blue Blue Blue Blue
Row 18: Blue Brown Blue Blue Blue Blue Brown Brown Brown Blue Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Brown Brown Blue
Row 20: Blue Brown Blue Blue Brown Blue Blue Blue Brown Brown Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown
Row 21: Blue Blue Blue Brown Brown Brown Brown Brown Blue Brown Blue Blue Blue Blue Brown Blue Blue Brown Blue Blue
Row 22: Blue Brown Brown Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Blue
Row 23: Brown Blue Blue Blue Brown Blue Blue Brown Blue Brown Brown Blue Brown Blue Blue Brown Blue Brown Brown Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Brown Blue Brown Blue Blue Blue Blue Blue Brown Blue Blue Brown Blue Brown Brown Brown Brown Brown Blue
Blue Blue Red Brown Brown Blue Blue Blue Blue Blue Brown Blue Blue Brown Blue Blue Blue Blue Brown Blue
Blue Blue Red Blue Blue Brown Brown Blue Blue Brown Brown Brown Blue Brown Brown Blue Brown Blue Blue Brown
Blue Brown Green Brown Blue Blue Blue Brown Blue Brown Brown Blue Blue Blue Blue Brown Blue Brown Blue Brown
Brown Brown Green Blue Blue Brown Blue Brown Blue Blue Brown Brown Brown Blue Brown Brown Brown Brown Blue Blue
Blue Brown Green Blue Blue Brown Brown Brown Blue Brown Blue Blue Blue Blue Brown Blue Brown Brown Brown Brown
Brown Brown Green Blue Blue Blue Blue Brown Brown Blue Brown Blue Blue Blue Brown Blue Brown Blue Blue Blue
Blue Blue Green Blue Blue Blue Brown Blue Brown Brown Brown Brown Brown Brown Blue Blue Blue Brown Blue Brown
Blue Blue Green Brown Brown Blue Blue Brown Blue Brown Brown Blue Blue Blue Brown Brown Brown Blue Blue Brown
Blue Blue Green Blue Brown Blue Brown Brown Brown Brown Blue Blue Blue Brown Brown Blue Brown Brown Brown Brown
Brown Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue
Blue Blue Brown Blue Brown Brown Blue Blue Brown Brown Blue Brown Blue Blue Brown Brown Blue Blue Green Blue
Brown Blue Brown Blue Blue Blue Brown Blue Brown Blue Brown Blue Blue Brown Brown Blue Brown Blue Green Brown
Brown Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Green Blue
Brown Blue Brown Brown Blue Brown Blue Brown Blue Blue Brown Brown Blue Brown Blue Blue Blue Blue Green Blue
Brown Brown Blue Blue Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Green Blue
Blue Blue Brown Blue Blue Brown Brown Brown Blue Brown Blue Brown Blue Brown Blue Blue Blue Blue Blue Blue
Blue Brown Blue Blue Blue Blue Brown Brown Brown Blue Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Brown Brown Blue
Blue Brown Blue Blue Brown Blue Blue Blue Brown Brown Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown
Blue Blue Blue Brown Brown Brown Brown Brown Blue Brown Blue Blue Blue Blue Brown Blue Blue Brown Blue Blue
Blue Brown Brown Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Blue
Brown Blue Blue Blue Brown Blue Blue Brown Blue Brown Brown Blue Brown Blue Blue Brown Blue Brown Brown Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray
Row 2: Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Purple Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Green Green Green Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Green Green Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 7: Gray Green Green Green Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Green Green Green Yellow Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Green Green Green Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray
Row 10: Gray Green Green Green Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Blue Gray
Row 11: Gray Green Green Green Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray
Row 12: Gray Green Green Green Purple Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Purple
Row 13: Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Brown Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 15: Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Black Purple Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Orange Gray Gray Gray Gray
Row 19: Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Yellow Brown Gray Gray Gray Gray Gray Gray Brown
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray
Row 2: Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Purple Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray
Row 7: Gray Green Green Green Red Red Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray
Row 10: Gray Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray
Row 11: Gray Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray
Row 12: Gray Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Gray Black Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Brown Gray Gray Gray Gray Gray Gray
Row 14: Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 15: Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Black Purple Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Orange Gray Gray Gray Gray
Row 19: Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Yellow Brown Gray Gray Gray Gray Gray Gray Brown
Example 2
Input:
Row 1: Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple
Row 2: Black Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple
Row 4: Purple Orange Purple Pink Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple Black
Row 7: Purple Purple Purple Purple Purple Orange Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Orange
Row 8: Black Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Orange Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Black Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Black Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple
Row 2: Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Pink Pink Orange Black Black Purple Orange Purple Black Orange Orange Orange Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple
Row 4: Purple Orange Purple Pink Pink Orange Black Black Purple Orange Purple Black Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Orange Purple Purple Pink Orange Black Black Purple Orange Purple Black Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Pink Orange Black Black Purple Orange Purple Black Orange Purple Orange Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple Black
Row 7: Purple Purple Purple Purple Pink Orange Black Black Purple Orange Purple Black Orange Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Orange
Row 8: Black Purple Purple Purple Pink Purple Black Black Purple Orange Purple Black Orange Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Black Black Purple Orange Purple Black Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Black Black Purple Orange Purple Black Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Black Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Black Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Red Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Black
Row 8: Pink Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 11: Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Yellow Pink Pink Pink Yellow
Row 14: Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Black Yellow Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Red Black Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Black Red Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Red Black Red Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Black Red Pink Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Red Black Red Pink Black Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Black Red Pink Black Yellow Yellow Yellow Black
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Red Red Red Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Yellow
Row 14: Yellow Yellow Yellow Black Black Black Black Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Red Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Pink Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Red Black Yellow Yellow
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink
Row 11: Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink
Row 15: Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink
Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink
Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink
Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange
Row 3: Pink Pink Pink Pink Pink Pink Orange
Row 4: Pink Orange Orange Orange Orange Pink Orange
Row 5: Pink Orange Orange Orange Orange Pink Orange
Row 6: Pink Orange Orange Orange Orange Pink Orange
Row 7: Pink Orange Orange Orange Orange Pink Orange
Row 8: Pink Orange Orange Orange Orange Pink Orange
Row 9: Pink Orange Orange Orange Orange Pink Orange
Row 10: Pink Pink Orange Orange Pink Pink Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange
Row 3: Pink Pink Pink Pink Pink Pink Orange
Row 4: Pink Yellow Yellow Yellow Yellow Pink Orange
Row 5: Pink Yellow Yellow Yellow Yellow Pink Orange
Row 6: Pink Yellow Yellow Yellow Yellow Pink Orange
Row 7: Pink Yellow Yellow Yellow Yellow Pink Orange
Row 8: Pink Yellow Yellow Yellow Yellow Pink Orange
Row 9: Pink Yellow Yellow Yellow Yellow Pink Orange
Row 10: Pink Pink Yellow Yellow Pink Pink Orange
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 4: Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 5: Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 6: Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 7: Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 8: Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 9: Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 10: Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 11: Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 12: Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 13: Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 14: Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 15: Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 16: Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 17: Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 18: Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 19: Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 20: Brown Brown Brown Brown Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Brown Brown Brown Brown Brown Brown Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 4: Brown Brown Brown Brown Brown Brown Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 5: Brown Brown Brown Brown Brown Brown Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 6: Brown Brown Brown Brown Brown Brown Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 7: Brown Brown Brown Brown Brown Brown Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 8: Brown Brown Brown Brown Brown Brown Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 9: Brown Brown Brown Brown Brown Brown Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 10: Brown Brown Brown Brown Brown Brown Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 11: Brown Brown Brown Brown Brown Brown Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 12: Brown Brown Brown Brown Brown Brown Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 13: Brown Brown Brown Brown Brown Brown Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 14: Brown Brown Brown Brown Brown Brown Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 15: Brown Brown Brown Brown Brown Brown Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 16: Brown Brown Brown Brown Brown Brown Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 17: Brown Brown Brown Brown Brown Brown Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 18: Brown Brown Brown Brown Brown Brown Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 19: Brown Brown Brown Brown Brown Brown Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 20: Brown Brown Brown Brown Brown Brown Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Blue Blue Blue Blue Blue Blue Pink
Row 3: Pink Blue Pink Pink Pink Pink Blue Pink
Row 4: Pink Pink Pink Pink Pink Pink Blue Pink
Row 5: Pink Blue Pink Pink Pink Pink Blue Pink
Row 6: Pink Blue Blue Blue Blue Blue Blue Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Blue Blue Blue Blue Blue Blue Pink
Row 3: Yellow Blue Yellow Yellow Yellow Yellow Blue Pink
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Blue Pink
Row 5: Yellow Blue Yellow Yellow Yellow Yellow Blue Pink
Row 6: Pink Blue Blue Blue Blue Blue Blue Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Orange Orange
Row 5: Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange
Row 6: Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Yellow Orange
Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Orange Orange
Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange
Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Orange Orange
Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Orange Orange
Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Orange Orange
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange
Row 2: Gray Pink
Row 3: Pink Gray
Output:
Row 1: Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange
Row 3: Gray Gray Pink Pink
Row 4: Gray Gray Pink Pink
Row 5: Pink Pink Gray Gray
Row 6: Pink Pink Gray Gray
Example 2
Input:
Row 1: Orange Gray Orange
Row 2: Blue Red Blue
Row 3: Red Brown Orange
Row 4: Brown Brown Pink
Output:
Row 1: Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange
Row 6: Blue Blue Blue Blue Blue Red Red Red Red Red Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Red Red Red Red Red Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Red Red Red Red Red Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Red Red Red Red Red Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Red Red Red Red Red Blue Blue Blue Blue Blue
Row 11: Red Red Red Red Red Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange
Row 12: Red Red Red Red Red Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange
Row 13: Red Red Red Red Red Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange
Row 14: Red Red Red Red Red Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange
Row 15: Red Red Red Red Red Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink
Example 3
Input:
Row 1: Red Blue Pink
Row 2: Pink Orange Green
Row 3: Blue Brown Brown
Row 4: Green Green Green
Row 5: Brown Blue Red
Output:
Row 1: Red Red Red Red Red Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink
Row 2: Red Red Red Red Red Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink
Row 3: Red Red Red Red Red Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink
Row 4: Red Red Red Red Red Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink
Row 5: Red Red Red Red Red Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Green Green Green Green Green
Row 7: Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Green Green Green Green Green
Row 8: Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Green Green Green Green Green
Row 9: Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Green Green Green Green Green
Row 10: Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Green Green Green Green Green
Row 11: Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Red Red Red Red Red
Row 22: Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Red Red Red Red Red
Row 23: Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Red Red Red Red Red
Row 24: Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Red Red Red Red Red
Row 25: Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Red Red Red Red Red
Here is the input grid for the test example:
Input:
Row 1: Black Blue Blue Brown
Row 2: Green Green Yellow Red
Row 3: Red Brown Yellow Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown
Black Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown
Black Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown
Black Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown
Black Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown
Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red
Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red
Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red
Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red
Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red
Red Red Red Red Red Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown
Red Red Red Red Red Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown
Red Red Red Red Red Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown
Red Red Red Red Red Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown
Red Red Red Red Red Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Red Red Red Red Red Red Red Red Red Red Red
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Brown Brown Brown Brown Brown Brown Red Red Red Red Red Red Red Red Red Red Red
Row 6: Brown Brown Brown Brown Brown Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Brown Brown Brown Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Brown Brown Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Brown Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Pink
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Pink Pink
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink
Example 3
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Black Black Blue Blue Blue Blue Blue Blue Blue
Black Black Orange Orange Orange Orange Orange Orange Orange Orange
Black Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Gray Gray Gray Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Green Green Green Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Green Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Green Green Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Green Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Green Purple Blue Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Green Green Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Blue Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Blue Purple Green Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 3
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black Gray Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Gray
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Gray Pink Black Black Gray
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Pink Gray Pink Black Black Black Black Gray Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Pink Pink Pink Black Black Pink Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Pink Pink Black Black Black Pink Pink Pink Gray Black Pink Gray Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Pink Gray Pink Pink Black Black Gray Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black Black Gray Black Pink Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Gray Black Black Black Black Black Black Gray
Row 16: Black Black Black Black Black Black Black Black Black Black Pink Black Black Gray Black Black Black Black Black Black Pink Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Gray Gray Black Black Black Pink Black Black Black Pink
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black Pink Pink Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Pink Black Black Black Black Gray
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Gray Black Black Gray Gray Pink Black Black Pink Pink Black Gray Black Pink Gray Gray
Row 5: Black Black Black Black Black Black Black Black Gray Pink Pink Black Gray Black Gray Pink Pink Gray Black Black Black Black Pink Black
Row 6: Black Black Black Black Black Black Black Black Pink Black Gray Pink Pink Pink Pink Pink Gray Gray Pink Black Black Gray Pink Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Pink Pink Black Black Pink Gray Gray Gray Pink Pink Pink Black Gray
Row 8: Black Black Black Black Black Black Black Black Gray Black Black Pink Gray Black Black Gray Pink Pink Pink Gray Pink Pink Gray Gray
Row 9: Black Black Black Black Black Black Black Black Black Black Pink Gray Pink Black Gray Black Black Black Black Black Black Pink Black Pink
Row 10: Black Black Black Black Black Black Black Black Pink Gray Gray Gray Pink Black Pink Pink Gray Pink Gray Black Black Pink Gray Black
Row 11: Black Black Black Black Black Black Black Black Pink Pink Gray Gray Pink Black Gray Pink Pink Pink Black Gray Pink Pink Pink Black
Row 12: Black Black Black Black Black Black Black Black Black Pink Pink Pink Gray Black Pink Pink Pink Gray Black Pink Gray Gray Pink Pink
Row 13: Black Black Black Black Black Black Black Black Black Gray Pink Black Black Gray Pink Gray Pink Pink Black Pink Gray Gray Gray Pink
Row 14: Black Black Black Black Black Black Black Black Pink Black Pink Black Black Black Black Black Black Gray Black Pink Gray Pink Black Black
Row 15: Black Black Black Black Black Black Black Black Gray Gray Pink Pink Gray Pink Pink Pink Gray Black Black Gray Pink Black Black Gray
Row 16: Black Black Black Black Black Black Black Black Gray Black Pink Pink Pink Gray Gray Gray Pink Black Black Pink Pink Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Pink Gray Black Black Pink Gray Gray Pink Pink Pink Pink Pink Gray Black Pink
Row 18: Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Gray Pink Pink Gray Black Gray Black Pink Pink Gray
Row 19: Black Black Black Black Black Black Black Black Gray Gray Pink Black Gray Black Pink Pink Black Black Pink Gray Gray Black Black Gray
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Brown Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Brown Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Black Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Black Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Black Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Black Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Black Yellow Blue Yellow Yellow Black Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow
Yellow Yellow Black Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Black Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Black Yellow
Yellow Yellow Yellow Yellow Yellow Brown Blue Blue Yellow Brown Yellow Blue Yellow Yellow
Yellow Yellow Blue Yellow Brown Yellow Blue Blue Brown Yellow Yellow Yellow Yellow Yellow
Yellow Black Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Black Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Black Yellow Yellow
Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Black Yellow Yellow Blue Yellow Black Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Black Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Pink Yellow Yellow Pink Pink Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow
Row 8: Yellow Yellow Pink Yellow Yellow Yellow Pink Pink Yellow Yellow Pink Yellow Yellow Yellow Yellow Pink
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Pink Yellow Yellow Yellow Pink
Row 14: Pink Yellow Yellow Pink Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Pink Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Pink Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Pink
Row 19: Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Pink Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Pink Yellow Yellow Pink Yellow Yellow Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow
Row 24: Pink Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow
Row 26: Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Pink Yellow
Output:
Row 1: Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Green Pink Green Green Pink Pink Green
Row 3: Green Green Green Green Yellow Pink Yellow Yellow Yellow Green Pink Green Green Green Green Green
Row 4: Green Pink Pink Green Yellow Yellow Yellow Yellow Yellow Green Green Green Yellow Yellow Yellow Yellow
Row 5: Green Green Green Green Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Pink Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow Yellow Pink Yellow Yellow Yellow
Row 8: Yellow Yellow Pink Yellow Yellow Green Pink Pink Green Yellow Pink Yellow Yellow Yellow Yellow Pink
Row 9: Yellow Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Green Green Green Green Green Yellow Yellow Yellow Pink Yellow Yellow Pink Yellow Yellow Yellow Pink
Row 14: Pink Green Green Pink Green Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Pink Green Green Pink Green Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 16: Green Green Green Green Green Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Pink Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Pink
Row 19: Green Pink Green Yellow Green Green Green Green Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 20: Green Pink Green Yellow Green Pink Pink Green Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow
Row 21: Green Green Green Yellow Green Green Green Green Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Pink Yellow Green Pink Green Yellow Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow
Row 24: Pink Yellow Yellow Yellow Green Pink Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink
Row 25: Yellow Yellow Yellow Yellow Green Green Green Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow
Row 26: Yellow Pink Yellow Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Green Pink Pink Green Yellow Yellow Pink Yellow Yellow Yellow Yellow Pink Yellow
Example 2
Input:
Row 1: Pink Pink Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Pink Purple
Row 3: Purple Purple Purple Purple Purple Purple
Row 4: Pink Purple Purple Purple Purple Pink
Row 5: Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Pink Purple Purple
Row 8: Pink Purple Purple Pink Purple Purple
Row 9: Pink Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Pink Pink Purple Purple
Output:
Row 1: Pink Pink Green Purple Purple Purple
Row 2: Green Green Green Purple Pink Purple
Row 3: Purple Purple Purple Purple Purple Purple
Row 4: Pink Purple Purple Purple Purple Pink
Row 5: Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Green Green Green Purple
Row 7: Green Green Green Pink Green Purple
Row 8: Pink Green Green Pink Green Purple
Row 9: Pink Green Green Green Green Purple
Row 10: Green Green Purple Purple Purple Purple
Row 11: Purple Green Green Green Green Purple
Row 12: Purple Green Pink Pink Green Purple
Example 3
Input:
Row 1: Gray Black Black Black Black Gray Black Black Black Black Gray Black Black Black Black Black Black Gray Black Black Black Black Gray Black Black Black Black Gray
Row 2: Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Gray Black Black Gray Black Black Gray Black Black Black Gray Black Black Black
Row 3: Black Black Black Black Black Black Black Black Gray Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Gray Black Black Black Gray Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Gray Black Black Black Gray Gray Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Gray Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black
Row 8: Black Black Black Black Black Black Gray Black Black Black Gray Black Black Gray Gray Black Black Gray Black Black Gray Black Black Gray Black Black Black Gray
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Gray Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Gray Black Black Black Black Black Black Black Black Black Black Gray Gray Black Black Gray Black Black Black Black Gray Black Black Black Black Black Black Gray
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Gray
Row 13: Black Black Black Black Black Gray Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black
Row 15: Black Gray Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Gray Gray
Row 16: Black Black Black Black Gray Black Black Black Black Black Black Black Black Gray Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black
Row 17: Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Gray Black Black Gray Black Black Black Black Black Black
Row 18: Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 20: Gray Gray Black Black Black Black Gray Black Black Black Black Black Black Black Gray Black Black Black Black Gray Gray Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Gray Gray Black Black Gray
Row 22: Black Black Black Gray Black Black Black Gray Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black
Row 24: Gray Black Black Black Black Gray Black Black Gray Black Black Black Gray Black Black Black Black Black Black Black Gray Black Black Gray Gray Black Black Gray
Output:
Row 1: Gray Black Black Black Black Gray Black Black Black Black Gray Black Black Black Black Black Green Gray Green Black Black Black Gray Black Black Black Black Gray
Row 2: Black Black Black Gray Black Black Black Green Green Green Black Black Black Black Gray Black Green Gray Green Black Gray Black Black Black Gray Black Black Black
Row 3: Black Black Black Black Black Black Black Green Gray Green Black Gray Black Black Black Black Green Green Green Black Black Black Black Black Black Black Black Black
Row 4: Black Gray Black Black Black Gray Black Green Gray Green Black Black Black Green Green Green Green Black Green Green Green Green Black Black Black Gray Black Black
Row 5: Black Black Black Black Black Black Black Green Green Green Black Black Black Green Gray Gray Green Black Green Gray Gray Green Black Black Black Black Black Black
Row 6: Black Green Green Green Green Black Black Black Black Black Black Black Black Green Green Green Green Black Green Green Green Green Black Black Black Black Black Black
Row 7: Black Green Gray Gray Green Black Black Black Black Black Black Black Green Green Green Green Black Black Black Black Black Black Black Black Black Gray Black Black
Row 8: Black Green Green Green Green Black Gray Black Black Black Gray Black Green Gray Gray Green Black Gray Black Black Gray Black Black Gray Black Black Black Gray
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Green Green Green Green Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Gray Black Black Black Black Gray Black Green Green Green Green Black Black Black Black Black Black Black Black Black Black Black Black Green Green
Row 11: Gray Black Black Black Black Black Black Black Black Black Green Gray Gray Green Black Gray Black Black Black Black Gray Black Black Black Black Black Green Gray
Row 12: Black Black Black Black Green Green Green Green Black Black Green Green Green Green Black Black Black Black Black Black Black Black Black Gray Black Black Green Gray
Row 13: Black Black Black Black Green Gray Gray Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Green
Row 14: Black Black Black Black Green Green Green Green Black Black Black Gray Black Black Black Black Black Black Black Gray Black Black Black Black Black Green Green Green
Row 15: Black Gray Black Black Black Black Black Black Black Gray Black Black Green Green Green Green Black Gray Black Black Black Black Black Black Black Green Gray Gray
Row 16: Black Black Black Black Gray Black Black Black Black Black Black Black Green Gray Gray Green Black Black Black Black Black Black Black Gray Black Green Green Green
Row 17: Black Black Black Black Black Black Black Gray Black Black Black Black Green Green Green Green Black Black Gray Black Black Gray Black Black Black Black Black Black
Row 18: Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black
Row 19: Green Green Green Black Black Black Black Black Black Black Gray Black Black Black Black Black Gray Black Green Green Green Green Black Black Black Black Black Black
Row 20: Gray Gray Green Black Black Black Gray Black Black Black Black Black Black Black Gray Black Black Black Green Gray Gray Green Green Green Green Green Black Black
Row 21: Green Green Green Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Green Green Green Green Green Gray Gray Green Black Gray
Row 22: Black Black Black Gray Black Black Black Gray Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Green Green Green Green Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Green Green Green Green Black Black
Row 24: Gray Black Black Black Black Gray Black Black Gray Black Black Black Gray Black Black Black Black Black Black Black Gray Black Green Gray Gray Green Black Gray
Here is the input grid for the test example:
Input:
Row 1: Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Red Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Red Orange Orange Orange Orange Red Orange Orange Orange Orange Red
Row 4: Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange
Row 7: Red Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Red Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Red
Row 9: Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Red
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange
Row 13: Orange Red Red Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Red Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Green Orange Orange Orange Orange Orange Green Green Green Orange Orange Orange Orange
Red Green Green Green Green Orange Orange Green Red Green Orange Orange Orange Orange
Green Green Green Red Green Orange Orange Green Red Green Orange Orange Orange Red
Orange Orange Green Red Green Orange Orange Green Green Green Orange Orange Orange Orange
Orange Orange Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange
Green Green Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange
Red Green Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Green Green
Red Green Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Green Red
Green Green Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Green Red
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange
Green Green Green Green Orange Orange Orange Orange Orange Red Orange Orange Orange Orange
Green Red Red Green Orange Orange Red Orange Orange Orange Green Green Green Green
Green Green Green Green Orange Orange Orange Orange Orange Orange Green Red Red Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Green Green Pink Yellow Red Orange Blue Green Purple
Row 2: Yellow Pink Yellow Purple Purple Green Green Purple Green Red
Row 3: Gray Green Green Blue Gray Orange Pink Orange Yellow Red
Row 4: Green Red Orange Green Pink Pink Yellow Yellow Blue Gray
Row 5: Purple Gray Pink Purple Blue Blue Green Orange Red Orange
Row 6: Purple Gray Purple Pink Green Blue Orange Purple Gray Red
Row 7: Orange Gray Green Gray Blue Purple Red Pink Pink Green
Row 8: Blue Purple Purple Blue Gray Pink Red Orange Blue Gray
Row 9: Purple Red Red Purple Green Green Pink Green Purple Orange
Row 10: Gray Purple Purple Blue Orange Purple Gray Orange Pink Gray
Row 11: Pink Orange Gray Purple Red Gray Yellow Green Orange Purple
Row 12: Purple Pink Blue Gray Gray Gray Green Orange Green Green
Row 13: Pink Green Red Pink Green Yellow Gray Yellow Orange Orange
Row 14: Green Orange Purple Red Orange Orange Red Green Purple Yellow
Row 15: Gray Pink Yellow Blue Orange Orange Purple Blue Pink Orange
Row 16: Gray Pink Red Orange Blue Blue Gray Pink Blue Gray
Row 17: Green Yellow Orange Gray Purple Pink Orange Blue Green Blue
Row 18: Purple Blue Orange Blue Pink Gray Red Blue Blue Pink
Row 19: Purple Pink Gray Red Orange Purple Purple Blue Blue Purple
Output:
Row 1: Purple Orange Green Gray Blue Pink Red Yellow
Row 2: Purple Orange Green Gray Blue Pink Red Yellow
Row 3: Purple Orange Green Gray Blue Pink Red Yellow
Row 4: Purple Orange Green Gray Blue Pink Red Yellow
Row 5: Purple Orange Green Gray Blue Pink Red Yellow
Row 6: Purple Orange Green Gray Blue Pink Red Yellow
Row 7: Purple Orange Green Gray Blue Pink Red Yellow
Row 8: Purple Orange Green Gray Blue Pink Red Yellow
Row 9: Purple Orange Green Gray Blue Pink Red Yellow
Row 10: Purple Orange Green Gray Blue Pink Red Yellow
Row 11: Purple Orange Green Gray Blue Pink Red Yellow
Row 12: Purple Orange Green Gray Blue Pink Red Yellow
Row 13: Purple Orange Green Gray Blue Pink Red Black
Row 14: Purple Orange Green Gray Blue Pink Red Black
Row 15: Purple Orange Green Gray Blue Pink Red Black
Row 16: Purple Orange Green Gray Blue Pink Red Black
Row 17: Purple Orange Green Gray Blue Pink Red Black
Row 18: Purple Orange Green Gray Blue Pink Red Black
Row 19: Purple Orange Green Gray Blue Pink Black Black
Row 20: Purple Orange Green Gray Blue Pink Black Black
Row 21: Purple Orange Green Gray Blue Pink Black Black
Row 22: Purple Orange Green Gray Blue Pink Black Black
Row 23: Purple Orange Green Gray Blue Pink Black Black
Row 24: Purple Orange Green Gray Blue Pink Black Black
Row 25: Purple Orange Green Gray Blue Black Black Black
Row 26: Purple Orange Green Gray Black Black Black Black
Row 27: Purple Orange Green Black Black Black Black Black
Row 28: Purple Orange Black Black Black Black Black Black
Row 29: Purple Black Black Black Black Black Black Black
Row 30: Purple Black Black Black Black Black Black Black
Example 2
Input:
Row 1: Orange Pink Pink Orange Green Blue Pink Orange Orange Pink Blue Yellow Blue Yellow Gray Orange Purple Gray Green
Row 2: Blue Pink Orange Pink Yellow Gray Pink Orange Blue Brown Orange Gray Orange Purple Yellow Green Pink Gray Green
Row 3: Purple Orange Blue Green Yellow Blue Pink Orange Blue Green Brown Pink Gray Green Blue Pink Green Pink Pink
Row 4: Pink Red Pink Blue Orange Blue Pink Orange Pink Orange Blue Blue Green Blue Blue Blue Orange Yellow Yellow
Output:
Row 1: Pink Blue Orange Green Yellow Gray Purple Brown Red
Row 2: Pink Blue Orange Green Yellow Gray Purple Brown Black
Row 3: Pink Blue Orange Green Yellow Gray Purple Black Black
Row 4: Pink Blue Orange Green Yellow Gray Black Black Black
Row 5: Pink Blue Orange Green Yellow Gray Black Black Black
Row 6: Pink Blue Orange Green Yellow Gray Black Black Black
Row 7: Pink Blue Orange Green Yellow Black Black Black Black
Row 8: Pink Blue Orange Green Black Black Black Black Black
Row 9: Pink Blue Orange Green Black Black Black Black Black
Row 10: Pink Blue Orange Black Black Black Black Black Black
Row 11: Pink Blue Orange Black Black Black Black Black Black
Row 12: Pink Blue Orange Black Black Black Black Black Black
Row 13: Pink Blue Orange Black Black Black Black Black Black
Row 14: Pink Blue Orange Black Black Black Black Black Black
Row 15: Pink Blue Orange Black Black Black Black Black Black
Row 16: Pink Blue Black Black Black Black Black Black Black
Row 17: Pink Black Black Black Black Black Black Black Black
Example 3
Input:
Row 1: Gray
Row 2: Brown
Row 3: Gray
Row 4: Gray
Row 5: Yellow
Row 6: Green
Row 7: Brown
Row 8: Brown
Row 9: Gray
Row 10: Yellow
Row 11: Gray
Row 12: Yellow
Row 13: Yellow
Row 14: Yellow
Row 15: Gray
Output:
Row 1: Gray Yellow Brown Green
Row 2: Gray Yellow Brown Black
Row 3: Gray Yellow Brown Black
Row 4: Gray Yellow Black Black
Row 5: Gray Yellow Black Black
Row 6: Gray Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Green Green Yellow
Row 2: Green Green Green
Row 3: Gray Yellow Gray
Row 4: Yellow Yellow Brown
Row 5: Gray Green Yellow
Row 6: Yellow Green Green
Row 7: Brown Green Gray
Row 8: Brown Yellow Yellow
Row 9: Brown Brown Green
Row 10: Gray Brown Brown
Row 11: Yellow Brown Yellow
Row 12: Yellow Brown Green
Row 13: Yellow Brown Green
Row 14: Yellow Gray Gray
Row 15: Brown Yellow Brown
Row 16: Yellow Green Brown
Row 17: Green Yellow Gray
Row 18: Gray Brown Gray
Row 19: Yellow Yellow Yellow
Row 20: Green Green Green
Row 21: Brown Brown Yellow
Row 22: Green Green Brown
Row 23: Green Green Brown
Row 24: Gray Green Gray
Row 25: Brown Yellow Green
Row 26: Yellow Brown Gray
Row 27: Gray Green Green
Row 28: Brown Yellow Yellow
Row 29: Brown Yellow Gray
Row 30: Brown Gray Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Yellow Brown Gray
Green Yellow Brown Gray
Green Yellow Brown Gray
Green Yellow Brown Gray
Green Yellow Brown Gray
Green Yellow Brown Gray
Green Yellow Brown Gray
Green Yellow Brown Gray
Green Yellow Brown Gray
Green Yellow Brown Gray
Green Yellow Brown Gray
Green Yellow Brown Gray
Green Yellow Brown Gray
Green Yellow Brown Gray
Green Yellow Brown Gray
Green Yellow Brown Gray
Green Yellow Brown Black
Green Yellow Brown Black
Green Yellow Brown Black
Green Yellow Brown Black
Green Yellow Brown Black
Green Yellow Brown Black
Green Yellow Brown Black
Green Yellow Black Black
Green Yellow Black Black
Green Black Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Gray Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Gray Gray Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Example 2
Input:
Row 1: Black Orange Black Black Orange Black Black Gray Black Gray Black Orange Gray Purple Orange Black
Row 2: Black Black Black Black Black Orange Black Black Black Green Black Black Black Black Orange Orange
Row 3: Black Black Orange Black Black Black Orange Black Black Orange Purple Black Purple Orange Black Black
Row 4: Orange Black Black Black Black Orange Black Black Orange Black Black Black Black Black Black Black
Row 5: Orange Black Black Black Orange Black Black Orange Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Orange
Row 7: Black Orange Orange Black Black Orange Purple Black Black Orange Orange Orange Black Black Orange Black
Row 8: Black Black Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black
Output:
Row 1: Black Blue Black Black Blue Black Black Blue Black Gray Black Orange Gray Purple Orange Black
Row 2: Black Black Black Black Black Blue Black Black Black Green Black Black Black Black Orange Orange
Row 3: Black Black Blue Black Black Black Blue Black Black Orange Purple Black Purple Orange Black Black
Row 4: Orange Black Black Black Black Blue Black Black Blue Black Black Black Black Black Black Black
Row 5: Orange Black Black Black Blue Black Black Blue Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Blue
Row 7: Black Orange Orange Black Black Orange Purple Black Black Orange Orange Orange Black Black Blue Black
Row 8: Black Black Black Black Black Orange Black Black Black Orange Black Black Black Blue Black Black
Example 3
Input:
Row 1: Black Black Black Black Red Gray Black Black Black Black Black Black Black Black Black Orange Gray Black Black Black
Row 2: Black Black Black Black Black Red Black Gray Black Black Black Black Black Red Black Black Red Black Black Black
Row 3: Black Orange Black Black Black Black Black Red Black Black Black Black Black Black Red Black Black Red Black Black
Row 4: Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Red
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Red Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Red Black Black
Row 9: Black Black Black Black Black Green Black Black Black Black Black Green Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Red Black Black Black Orange Black Black Black Black Black Black Black Black Green Red Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black Black Black Black
Row 13: Gray Black Black Black Black Black Black Black Black Red Black Black Black Black Black Black Red Black Black Black
Row 14: Black Black Black Black Black Black Black Black Gray Black Black Red Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Red Red Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Red Gray Black Black Black Black Black Black Black Black Black Orange Gray Black Black Black
Row 2: Black Black Black Black Black Red Black Gray Black Black Black Black Black Blue Black Black Red Black Black Black
Row 3: Black Blue Black Black Black Black Black Red Black Black Black Black Black Black Blue Black Black Blue Black Black
Row 4: Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Blue
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Blue Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Blue Black Black
Row 9: Black Black Black Black Black Blue Black Black Black Black Black Blue Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Blue Black Black Black Blue Black Black Black Black Black Black Black Black Green Red Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black Black Black Black
Row 13: Blue Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Blue Black Black Black
Row 14: Black Black Black Black Black Black Black Black Blue Black Black Blue Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Red Red Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Black Black Black
Row 2: Black Black Black
Row 3: Black Black Black
Row 4: Black Black Black
Row 5: Green Black Black
Row 6: Orange Black Black
Row 7: Yellow Black Black
Row 8: Black Black Black
Row 9: Black Black Black
Row 10: Yellow Black Pink
Row 11: Black Black Black
Row 12: Black Green Black
Row 13: Black Black Black
Row 14: Black Red Pink
Row 15: Black Black Black
Row 16: Black Black Black
Row 17: Black Black Green
Row 18: Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Black Black
Black Black Black
Black Black Black
Black Black Black
Green Black Black
Orange Black Black
Yellow Black Black
Black Black Black
Black Black Black
Blue Black Blue
Black Black Black
Black Blue Black
Black Black Black
Black Red Pink
Black Black Black
Black Black Black
Black Black Blue
Black Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Purple Purple Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Purple Purple Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Blue Orange Orange Red Orange Orange Orange Orange
Row 5: Orange Orange Orange Purple Purple Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Purple Purple Orange Orange Orange Orange Orange
Row 7: Orange Orange Green Orange Orange Yellow Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Orange Orange Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Orange Orange Black Black Black Black Black Orange Orange Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Orange Orange Black Black Black Black Black Black Black
Row 7: Black Black Orange Orange Black Black Black Orange Orange Black Black Black Black Black Black Black
Row 8: Black Black Orange Orange Black Black Black Black Black Black Black Black Orange Orange Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Orange Orange Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Orange Orange Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Orange Orange Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Orange Orange Black Black Orange Orange Black Black Black Orange Orange Black Black Black Black
Row 16: Black Black Black Black Black Orange Orange Black Black Black Orange Orange Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Blue Black Black Red Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Orange Orange Black Black Black Black Blue Black Black Red
Row 3: Black Black Black Black Black Black Orange Orange Black Black Black Black Black Orange Orange Black
Row 4: Black Black Black Black Black Green Black Black Yellow Black Black Black Black Orange Orange Black
Row 5: Black Black Black Black Black Black Blue Black Black Red Black Black Green Black Black Yellow
Row 6: Black Blue Black Black Red Black Black Orange Orange Black Black Black Black Black Black Black
Row 7: Black Black Orange Orange Black Black Black Orange Orange Black Black Blue Black Black Red Black
Row 8: Black Black Orange Orange Black Black Green Black Black Yellow Black Black Orange Orange Black Black
Row 9: Black Green Black Black Yellow Black Black Black Black Black Black Black Orange Orange Black Black
Row 10: Black Black Black Black Black Black Blue Black Black Red Black Green Black Black Yellow Black
Row 11: Black Black Black Black Black Black Black Orange Orange Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Orange Orange Black Black Black Black Black Black Black
Row 13: Blue Black Black Red Black Black Green Black Black Yellow Black Black Black Black Black Black
Row 14: Black Orange Orange Black Blue Black Black Red Black Blue Black Black Red Black Black Black
Row 15: Black Orange Orange Black Black Orange Orange Black Black Black Orange Orange Black Black Black Black
Row 16: Green Black Black Yellow Black Orange Orange Black Black Black Orange Orange Black Black Black Black
Row 17: Black Black Black Black Green Black Black Yellow Black Green Black Black Yellow Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Example 3
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Orange Orange Gray Gray Gray Gray Gray Gray Orange Orange Gray Gray Gray Gray Orange Orange Gray Gray
Row 5: Gray Orange Orange Gray Gray Orange Orange Gray Gray Orange Orange Gray Gray Gray Gray Orange Orange Gray Gray
Row 6: Gray Gray Gray Gray Gray Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray Gray Gray Gray
Row 9: Gray Gray Orange Orange Gray Gray Gray Gray Gray Orange Orange Gray Gray Orange Orange Gray Gray Gray Gray
Row 10: Gray Gray Orange Orange Gray Gray Gray Gray Gray Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Orange Orange Gray Gray Orange Orange Gray Gray Gray Orange Orange Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Orange Orange Gray Gray Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Orange Orange Gray Gray Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Orange Orange Gray Gray Orange Orange Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray Gray Gray Orange Orange Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Blue Gray Gray Red Gray Gray Gray Gray Blue Gray Gray Red Gray Gray Blue Gray Gray Red Gray
Row 4: Gray Orange Orange Gray Blue Gray Gray Red Gray Orange Orange Gray Gray Gray Gray Orange Orange Gray Gray
Row 5: Gray Orange Orange Gray Gray Orange Orange Gray Gray Orange Orange Gray Gray Gray Gray Orange Orange Gray Gray
Row 6: Green Gray Gray Yellow Gray Orange Orange Gray Green Gray Gray Yellow Gray Gray Green Gray Gray Yellow Gray
Row 7: Gray Gray Gray Gray Green Gray Gray Yellow Gray Gray Gray Gray Blue Gray Gray Red Gray Gray Gray
Row 8: Gray Blue Gray Gray Red Gray Gray Gray Blue Gray Gray Red Gray Orange Orange Gray Gray Gray Gray
Row 9: Gray Gray Orange Orange Gray Gray Gray Gray Gray Orange Orange Gray Gray Orange Orange Gray Gray Gray Gray
Row 10: Gray Gray Orange Orange Gray Gray Gray Gray Gray Orange Orange Gray Green Gray Gray Yellow Gray Gray Gray
Row 11: Gray Green Gray Gray Yellow Gray Gray Gray Green Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Red Gray Gray Gray Gray Gray
Row 13: Gray Blue Gray Gray Red Blue Gray Gray Red Gray Gray Orange Orange Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Orange Orange Gray Gray Orange Orange Gray Gray Gray Orange Orange Gray Gray Blue Gray Gray Red
Row 15: Gray Gray Orange Orange Gray Gray Orange Orange Gray Gray Green Gray Gray Yellow Gray Gray Orange Orange Gray
Row 16: Gray Green Gray Gray Yellow Green Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray
Row 17: Gray Blue Gray Gray Red Blue Gray Gray Red Gray Gray Gray Gray Gray Gray Green Gray Gray Yellow
Row 18: Gray Gray Orange Orange Gray Gray Orange Orange Gray Gray Gray Gray Gray Gray Blue Gray Gray Red Gray
Row 19: Gray Gray Orange Orange Gray Gray Orange Orange Gray Blue Gray Gray Red Gray Gray Orange Orange Gray Gray
Row 20: Gray Green Gray Gray Yellow Green Gray Gray Yellow Gray Orange Orange Gray Gray Gray Orange Orange Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray Gray Green Gray Gray Yellow Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Yellow Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Purple Purple Brown Brown Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Blue Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Red Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Purple Blue Purple Purple Red Purple
Purple Purple Purple Purple Purple Brown Brown Purple Blue Purple Purple Red Purple Purple Purple Purple Purple Purple Brown Brown Purple Purple Brown Brown Purple Purple
Purple Purple Purple Purple Green Purple Purple Yellow Purple Brown Brown Purple Purple Purple Purple Purple Purple Green Purple Purple Yellow Purple Brown Brown Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Yellow Purple
Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Yellow Yellow Yellow Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Example 3
Input:
Row 1: Blue Blue Blue Blue Blue Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Blue Blue Blue Blue Blue Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Blue Blue Blue Blue Blue Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Black Black Black Black Black Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 27: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 28: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 29: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 30: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Yellow Yellow
Row 2: Red Red Red Yellow Yellow Yellow Purple Purple Purple Yellow Yellow
Row 3: Red Red Red Yellow Yellow Yellow Purple Purple Purple Yellow Yellow
Row 4: Red Red Red Yellow Yellow Yellow Purple Purple Purple Yellow Yellow
Row 5: Red Red Red Yellow Yellow Yellow Purple Purple Purple Yellow Yellow
Row 6: Red Red Red Yellow Yellow Yellow Purple Purple Purple Yellow Yellow
Row 7: Red Red Red Yellow Yellow Yellow Purple Purple Purple Yellow Yellow
Row 8: Red Red Red Yellow Yellow Yellow Purple Purple Purple Yellow Yellow
Row 9: Red Red Red Yellow Yellow Yellow Purple Purple Purple Yellow Yellow
Row 10: Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Yellow Yellow
Row 2: Red Red Red Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow
Row 3: Red Yellow Red Yellow Yellow Yellow Purple Purple Purple Yellow Yellow
Row 4: Red Red Red Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow
Row 5: Red Yellow Red Yellow Yellow Yellow Purple Purple Purple Yellow Yellow
Row 6: Red Red Red Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow
Row 7: Red Yellow Red Yellow Yellow Yellow Purple Purple Purple Yellow Yellow
Row 8: Red Red Red Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow
Row 9: Red Yellow Red Yellow Yellow Yellow Purple Purple Purple Yellow Yellow
Row 10: Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Blue Blue Blue Orange Orange Orange Brown Brown Brown Orange Red Red Red Orange Orange Orange Pink Pink Pink Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Blue Blue Blue Orange Orange Orange Brown Brown Brown Orange Red Red Red Yellow Yellow Yellow Pink Pink Pink Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Blue Blue Blue Orange Orange Orange Brown Brown Brown Orange Red Red Red Yellow Yellow Yellow Pink Pink Pink Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Red Red Red Yellow Yellow Yellow Pink Pink Pink Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Red Red Red Yellow Yellow Yellow Pink Pink Pink Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Pink Pink Pink Orange Orange Orange Orange
Row 9: Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Yellow Yellow Yellow Pink Pink Pink Orange Orange Orange Orange
Row 10: Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Yellow Yellow Yellow Pink Pink Pink Orange Orange Orange Orange
Row 11: Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Brown Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Blue Blue Blue Orange Orange Orange Brown Brown Brown Orange Red Red Red Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Blue Orange Blue Orange Orange Orange Brown Orange Brown Orange Red Orange Red Yellow Yellow Yellow Pink Pink Pink Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Blue Blue Blue Orange Orange Orange Brown Brown Brown Orange Red Red Red Yellow Orange Yellow Pink Orange Pink Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Blue Orange Blue Orange Orange Orange Orange Orange Orange Orange Red Orange Red Yellow Yellow Yellow Pink Pink Pink Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Red Red Red Yellow Orange Yellow Pink Orange Pink Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Pink Pink Pink Orange Orange Orange Orange
Row 9: Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Yellow Orange Yellow Pink Orange Pink Orange Orange Orange Orange
Row 10: Orange Green Orange Green Orange Green Orange Green Orange Green Orange Green Orange Green Orange Green Orange Green Orange Yellow Yellow Yellow Pink Pink Pink Orange Orange Orange Orange
Row 11: Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Gray Purple Gray Purple Gray Purple Gray Purple Gray Purple Gray Purple Gray Purple Gray Purple Gray Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Green Green Purple Purple Purple Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green
Row 2: Green Green Purple Purple Purple Yellow Yellow Yellow Green Green Green Green Gray Gray Gray Green Green
Row 3: Green Green Purple Purple Purple Yellow Yellow Yellow Green Green Green Green Gray Gray Gray Green Green
Row 4: Green Green Purple Purple Purple Yellow Yellow Yellow Green Green Green Green Gray Gray Gray Green Green
Row 5: Green Green Purple Purple Purple Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green
Row 7: Green Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green
Row 8: Green Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green
Row 9: Green Blue Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Green Purple Purple Purple Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green
Green Green Purple Green Purple Yellow Green Yellow Green Green Green Green Gray Gray Gray Green Green
Green Green Purple Purple Purple Yellow Yellow Yellow Green Green Green Green Gray Green Gray Green Green
Green Green Purple Green Purple Yellow Green Yellow Green Green Green Green Gray Gray Gray Green Green
Green Green Purple Purple Purple Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green
Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green
Green Blue Blue Blue Orange Green Orange Green Orange Green Orange Green Orange Green Green Green Green
Green Blue Green Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green
Green Blue Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Brown Brown Brown Brown Brown Purple
Row 3: Purple Brown Brown Brown Brown Brown Purple
Row 4: Purple Brown Gray Gray Gray Brown Purple
Row 5: Purple Brown Gray Gray Gray Brown Purple
Row 6: Purple Brown Gray Black Gray Brown Purple
Row 7: Purple Brown Gray Gray Gray Brown Purple
Row 8: Purple Brown Brown Brown Brown Brown Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Brown Brown Brown Brown Brown Purple
Row 3: Purple Brown Gray Gray Gray Brown Purple
Row 4: Purple Brown Gray Black Gray Brown Purple
Row 5: Purple Brown Gray Gray Gray Brown Purple
Row 6: Purple Brown Brown Brown Brown Brown Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray
Row 3: Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray
Row 4: Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray
Row 5: Gray Yellow Yellow Red Red Red Red Red Red Red Red Red Red Yellow Gray
Row 6: Gray Yellow Yellow Red Pink Pink Pink Pink Pink Pink Pink Pink Red Yellow Gray
Row 7: Gray Yellow Yellow Red Pink Pink Pink Pink Pink Pink Pink Pink Red Yellow Gray
Row 8: Gray Yellow Yellow Red Pink Pink Pink Pink Pink Pink Pink Pink Red Yellow Gray
Row 9: Gray Yellow Yellow Red Pink Pink Pink Pink Pink Pink Pink Pink Red Yellow Gray
Row 10: Gray Yellow Yellow Red Pink Pink Pink Pink Pink Pink Pink Pink Red Yellow Gray
Row 11: Gray Yellow Yellow Red Pink Pink Pink Pink Pink Pink Pink Pink Red Yellow Gray
Row 12: Gray Yellow Yellow Red Pink Pink Purple Purple Purple Purple Purple Pink Red Yellow Gray
Row 13: Gray Yellow Yellow Red Pink Pink Purple Blue Blue Blue Purple Pink Red Yellow Gray
Row 14: Gray Yellow Yellow Red Pink Pink Purple Blue Blue Blue Purple Pink Red Yellow Gray
Row 15: Gray Yellow Yellow Red Pink Pink Purple Blue Blue Blue Purple Pink Red Yellow Gray
Row 16: Gray Yellow Yellow Red Pink Pink Purple Blue Blue Blue Purple Pink Red Yellow Gray
Row 17: Gray Yellow Yellow Red Pink Pink Purple Blue Blue Blue Purple Pink Red Yellow Gray
Row 18: Gray Yellow Yellow Red Pink Pink Purple Blue Blue Blue Purple Pink Red Yellow Gray
Row 19: Gray Yellow Yellow Red Pink Pink Purple Purple Purple Purple Purple Pink Red Yellow Gray
Row 20: Gray Yellow Yellow Red Pink Pink Pink Pink Pink Pink Pink Pink Red Yellow Gray
Row 21: Gray Yellow Yellow Red Pink Pink Pink Pink Pink Pink Pink Pink Red Yellow Gray
Row 22: Gray Yellow Yellow Red Red Red Red Red Red Red Red Red Red Yellow Gray
Row 23: Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray
Row 24: Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray
Row 25: Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray
Row 26: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 27: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray
Row 3: Gray Yellow Red Red Red Red Red Red Red Yellow Gray
Row 4: Gray Yellow Red Pink Pink Pink Pink Pink Red Yellow Gray
Row 5: Gray Yellow Red Pink Purple Purple Purple Pink Red Yellow Gray
Row 6: Gray Yellow Red Pink Purple Blue Purple Pink Red Yellow Gray
Row 7: Gray Yellow Red Pink Purple Purple Purple Pink Red Yellow Gray
Row 8: Gray Yellow Red Pink Pink Pink Pink Pink Red Yellow Gray
Row 9: Gray Yellow Red Red Red Red Red Red Red Yellow Gray
Row 10: Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Example 3
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 3: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 4: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 5: Black Black Blue Blue Blue Red Red Red Red Red Red Red Red Red Blue Black
Row 6: Black Black Blue Blue Blue Red Red Red Red Red Red Red Red Red Blue Black
Row 7: Black Black Blue Blue Blue Red Red Red Red Red Red Red Red Red Blue Black
Row 8: Black Black Blue Blue Blue Red Red Red Red Red Red Red Red Red Blue Black
Row 9: Black Black Blue Blue Blue Red Red Red Red Red Red Red Red Red Blue Black
Row 10: Black Black Blue Blue Blue Red Green Green Green Green Green Green Green Red Blue Black
Row 11: Black Black Blue Blue Blue Red Green Purple Purple Purple Purple Purple Green Red Blue Black
Row 12: Black Black Blue Blue Blue Red Green Purple Purple Purple Purple Purple Green Red Blue Black
Row 13: Black Black Blue Blue Blue Red Green Purple Purple Brown Purple Purple Green Red Blue Black
Row 14: Black Black Blue Blue Blue Red Green Purple Purple Brown Purple Purple Green Red Blue Black
Row 15: Black Black Blue Blue Blue Red Green Purple Purple Purple Purple Purple Green Red Blue Black
Row 16: Black Black Blue Blue Blue Red Green Purple Purple Purple Purple Purple Green Red Blue Black
Row 17: Black Black Blue Blue Blue Red Green Purple Purple Purple Purple Purple Green Red Blue Black
Row 18: Black Black Blue Blue Blue Red Green Purple Purple Purple Purple Purple Green Red Blue Black
Row 19: Black Black Blue Blue Blue Red Green Green Green Green Green Green Green Red Blue Black
Row 20: Black Black Blue Blue Blue Red Red Red Red Red Red Red Red Red Blue Black
Row 21: Black Black Blue Blue Blue Red Red Red Red Red Red Red Red Red Blue Black
Row 22: Black Black Blue Blue Blue Red Red Red Red Red Red Red Red Red Blue Black
Row 23: Black Black Blue Blue Blue Red Red Red Red Red Red Red Red Red Blue Black
Row 24: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 25: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 26: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 27: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 28: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 3: Black Blue Red Red Red Red Red Red Red Blue Black
Row 4: Black Blue Red Green Green Green Green Green Red Blue Black
Row 5: Black Blue Red Green Purple Purple Purple Green Red Blue Black
Row 6: Black Blue Red Green Purple Brown Purple Green Red Blue Black
Row 7: Black Blue Red Green Purple Purple Purple Green Red Blue Black
Row 8: Black Blue Red Green Green Green Green Green Red Blue Black
Row 9: Black Blue Red Red Red Red Red Red Red Blue Black
Row 10: Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 4: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 5: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 6: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 7: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 8: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 9: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 10: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 11: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 12: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 13: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 14: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 15: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 16: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 17: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 18: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 19: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 20: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 21: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 22: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 23: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 24: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 25: Orange Orange Orange Orange Pink Purple Purple Pink Orange Orange
Row 26: Orange Orange Orange Orange Pink Purple Purple Pink Orange Orange
Row 27: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 28: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 29: Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange
Row 30: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Orange Orange Orange Orange
Orange Pink Pink Pink Orange
Orange Pink Purple Pink Orange
Orange Pink Pink Pink Orange
Orange Orange Orange Orange Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Blue Pink
Row 2: Green Purple Green
Row 3: Red Green Gray
Row 4: Green Green Yellow
Output:
Row 1: Green Blue Pink Black Black Black Black Black Black
Row 2: Green Purple Green Black Black Black Black Black Black
Row 3: Red Green Gray Black Black Black Black Black Black
Row 4: Green Green Yellow Black Black Black Black Black Black
Row 5: Green Blue Pink Black Black Black Green Blue Pink
Row 6: Green Purple Green Black Black Black Green Purple Green
Row 7: Red Green Gray Black Black Black Red Green Gray
Row 8: Green Green Yellow Black Black Black Green Green Yellow
Row 9: Black Black Black Green Blue Pink Black Black Black
Row 10: Black Black Black Green Purple Green Black Black Black
Row 11: Black Black Black Red Green Gray Black Black Black
Row 12: Black Black Black Green Green Yellow Black Black Black
Row 13: Green Blue Pink Green Blue Pink Black Black Black
Row 14: Green Purple Green Green Purple Green Black Black Black
Row 15: Red Green Gray Red Green Gray Black Black Black
Row 16: Green Green Yellow Green Green Yellow Black Black Black
Example 2
Input:
Row 1: Green Green
Row 2: Green Green
Row 3: Green Pink
Row 4: Green Green
Row 5: Green Green
Output:
Row 1: Green Green Green Green
Row 2: Green Green Green Green
Row 3: Green Pink Green Pink
Row 4: Green Green Green Green
Row 5: Green Green Green Green
Row 6: Green Green Green Green
Row 7: Green Green Green Green
Row 8: Green Pink Green Pink
Row 9: Green Green Green Green
Row 10: Green Green Green Green
Row 11: Green Green Black Black
Row 12: Green Green Black Black
Row 13: Green Pink Black Black
Row 14: Green Green Black Black
Row 15: Green Green Black Black
Row 16: Green Green Green Green
Row 17: Green Green Green Green
Row 18: Green Pink Green Pink
Row 19: Green Green Green Green
Row 20: Green Green Green Green
Row 21: Green Green Green Green
Row 22: Green Green Green Green
Row 23: Green Pink Green Pink
Row 24: Green Green Green Green
Row 25: Green Green Green Green
Example 3
Input:
Row 1: Brown Pink Green
Row 2: Green Green Green
Row 3: Red Green Green
Row 4: Green Pink Brown
Output:
Row 1: Black Black Black Black Black Black Brown Pink Green
Row 2: Black Black Black Black Black Black Green Green Green
Row 3: Black Black Black Black Black Black Red Green Green
Row 4: Black Black Black Black Black Black Green Pink Brown
Row 5: Brown Pink Green Brown Pink Green Brown Pink Green
Row 6: Green Green Green Green Green Green Green Green Green
Row 7: Red Green Green Red Green Green Red Green Green
Row 8: Green Pink Brown Green Pink Brown Green Pink Brown
Row 9: Black Black Black Brown Pink Green Brown Pink Green
Row 10: Black Black Black Green Green Green Green Green Green
Row 11: Black Black Black Red Green Green Red Green Green
Row 12: Black Black Black Green Pink Brown Green Pink Brown
Row 13: Brown Pink Green Black Black Black Black Black Black
Row 14: Green Green Green Black Black Black Black Black Black
Row 15: Red Green Green Black Black Black Black Black Black
Row 16: Green Pink Brown Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Yellow Red Red
Row 2: Red Green Red
Row 3: Pink Brown Red
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Black Black Yellow Red Red Yellow Red Red
Black Black Black Red Green Red Red Green Red
Black Black Black Pink Brown Red Pink Brown Red
Yellow Red Red Black Black Black Yellow Red Red
Red Green Red Black Black Black Red Green Red
Pink Brown Red Black Black Black Pink Brown Red
Black Black Black Black Black Black Yellow Red Red
Black Black Black Black Black Black Red Green Red
Black Black Black Black Black Black Pink Brown Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Blue Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Purple Yellow Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Yellow Yellow Purple Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Purple Yellow Purple Yellow Purple Yellow Purple Purple Yellow Purple Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Purple Yellow Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Yellow Purple Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Blue Yellow Blue Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Blue Yellow Blue Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Purple Yellow Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Yellow Purple Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Purple Yellow Purple Yellow Purple Yellow Purple Purple Yellow Purple Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Yellow Yellow Purple Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 2
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Brown Green Brown Green Green Green Green Green
Row 5: Green Green Green Green Brown Green Green Green Green Green Green
Row 6: Green Green Green Brown Green Brown Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Red Green Green Green
Row 8: Green Green Green Green Green Red Green Red Green Green Green
Row 9: Green Green Green Green Green Red Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Red Green Red Green Green Green Green Green
Row 2: Green Red Green Red Green Red Green Red Green Green Green
Row 3: Green Red Green Green Green Green Green Red Green Green Green
Row 4: Green Green Green Brown Green Brown Green Green Green Green Green
Row 5: Green Green Green Green Brown Green Green Green Green Green Green
Row 6: Green Green Green Brown Green Brown Green Green Green Green Green
Row 7: Green Red Green Green Green Green Green Red Green Green Green
Row 8: Green Red Green Red Green Red Green Red Green Green Green
Row 9: Green Green Green Red Green Red Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Blue Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Pink Pink Pink Pink Pink Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Blue Pink Blue Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Blue Pink Blue Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Pink Pink Pink Pink Pink Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Green Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Green Purple Purple Pink Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Pink Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Green Purple Green Green Purple Green Green Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Green Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Green Purple Purple Pink Purple Pink Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Green Purple Purple Pink Purple Pink Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Green Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Green Purple Green Green Purple Green Green Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black
Row 5: Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Orange Black Black Black
Row 6: Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Orange Black Black Black
Row 7: Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black
Row 3: Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black
Row 4: Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black
Row 5: Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black
Row 6: Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black
Row 7: Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black
Row 8: Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black
Row 9: Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink
Row 3: Pink Orange Blue Blue Blue Blue Blue Blue Blue Blue Orange Pink
Row 4: Pink Orange Blue Blue Blue Blue Blue Blue Blue Blue Orange Pink
Row 5: Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 3: Blue Orange Pink Pink Pink Pink Pink Pink Pink Pink Orange Blue
Row 4: Blue Orange Pink Pink Pink Pink Pink Pink Pink Pink Orange Blue
Row 5: Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Example 3
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Black
Row 4: Black Black Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Black Black
Row 5: Black Black Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Black Black
Row 6: Black Black Pink Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Pink Black Black
Row 7: Black Black Pink Red Red Pink Gray Gray Gray Gray Gray Gray Gray Gray Pink Red Red Pink Black Black
Row 8: Black Black Pink Red Red Pink Gray Orange Orange Orange Orange Orange Orange Gray Pink Red Red Pink Black Black
Row 9: Black Black Pink Red Red Pink Gray Orange Purple Purple Purple Purple Orange Gray Pink Red Red Pink Black Black
Row 10: Black Black Pink Red Red Pink Gray Orange Purple Purple Purple Purple Orange Gray Pink Red Red Pink Black Black
Row 11: Black Black Pink Red Red Pink Gray Orange Purple Purple Purple Purple Orange Gray Pink Red Red Pink Black Black
Row 12: Black Black Pink Red Red Pink Gray Orange Purple Purple Purple Purple Orange Gray Pink Red Red Pink Black Black
Row 13: Black Black Pink Red Red Pink Gray Orange Orange Orange Orange Orange Orange Gray Pink Red Red Pink Black Black
Row 14: Black Black Pink Red Red Pink Gray Gray Gray Gray Gray Gray Gray Gray Pink Red Red Pink Black Black
Row 15: Black Black Pink Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Pink Black Black
Row 16: Black Black Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Black Black
Row 17: Black Black Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Black Black
Row 18: Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple
Row 4: Purple Purple Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Purple Purple
Row 5: Purple Purple Orange Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Orange Purple Purple
Row 6: Purple Purple Orange Gray Pink Red Red Red Red Red Red Red Red Red Red Pink Gray Orange Purple Purple
Row 7: Purple Purple Orange Gray Pink Red Red Red Red Red Red Red Red Red Red Pink Gray Orange Purple Purple
Row 8: Purple Purple Orange Gray Pink Red Red Pink Pink Pink Pink Pink Pink Red Red Pink Gray Orange Purple Purple
Row 9: Purple Purple Orange Gray Pink Red Red Pink Black Black Black Black Pink Red Red Pink Gray Orange Purple Purple
Row 10: Purple Purple Orange Gray Pink Red Red Pink Black Black Black Black Pink Red Red Pink Gray Orange Purple Purple
Row 11: Purple Purple Orange Gray Pink Red Red Pink Black Black Black Black Pink Red Red Pink Gray Orange Purple Purple
Row 12: Purple Purple Orange Gray Pink Red Red Pink Black Black Black Black Pink Red Red Pink Gray Orange Purple Purple
Row 13: Purple Purple Orange Gray Pink Red Red Pink Pink Pink Pink Pink Pink Red Red Pink Gray Orange Purple Purple
Row 14: Purple Purple Orange Gray Pink Red Red Red Red Red Red Red Red Red Red Pink Gray Orange Purple Purple
Row 15: Purple Purple Orange Gray Pink Red Red Red Red Red Red Red Red Red Red Pink Gray Orange Purple Purple
Row 16: Purple Purple Orange Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Orange Purple Purple
Row 17: Purple Purple Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Purple Purple
Row 18: Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Black Black Pink Pink
Row 4: Pink Pink Black Black Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Black Black Black Black Black
Black Pink Pink Pink Pink Black
Black Pink Pink Pink Pink Black
Black Pink Pink Pink Pink Black
Black Pink Pink Pink Pink Black
Black Black Black Black Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Red Blue Red Blue Red Blue Red Red Red Red Blue Red Red Blue Red Red Red Red Blue Red Blue Brown Brown Blue
Row 2: Red Blue Red Blue Blue Red Blue Red Blue Red Red Blue Blue Blue Blue Blue Blue Red Red Blue Blue Blue Blue Blue Blue Brown
Row 3: Red Blue Blue Red Blue Blue Blue Blue Blue Blue Red Red Red Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Brown
Row 4: Red Red Blue Blue Blue Red Red Red Blue Red Blue Blue Blue Blue Red Blue Red Red Blue Blue Red Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Red Blue Blue Red Blue Blue Red Red Red Red Red Blue Blue Red Red Red Red Blue Red Blue Brown Brown Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Brown Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Brown Blue Blue Blue Blue Brown Brown
Row 10: Brown Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Brown Blue Blue Blue Blue Blue Brown Blue Brown Blue Brown Blue Brown Brown Brown
Output:
Row 1: Red Red Red Blue Red Blue Red Blue Red Red Red Red Blue Red Red Blue Red Red Red Red Blue Red
Row 2: Red Blue Red Blue Blue Red Blue Red Blue Red Red Blue Blue Blue Blue Blue Blue Red Red Blue Blue Blue
Row 3: Red Blue Blue Red Blue Blue Blue Blue Blue Blue Red Red Red Blue Blue Blue Blue Blue Red Blue Blue Blue
Row 4: Red Red Blue Blue Blue Red Red Red Blue Red Blue Blue Blue Blue Red Blue Red Red Blue Blue Red Blue
Row 5: Blue Blue Blue Red Blue Blue Red Blue Blue Red Red Red Red Red Blue Blue Red Red Red Red Blue Red
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Brown Blue Blue Blue Blue Brown Brown Brown Brown Blue Blue Blue Blue Blue Brown Brown
Row 2: Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Blue Brown Brown Brown Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Blue Brown Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Brown Brown Brown Brown Blue Brown Blue Blue Blue Brown Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Brown Brown Brown Brown Blue Blue Blue Brown Blue Brown Brown
Row 6: Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Brown
Row 7: Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Blue Brown Blue Blue Blue Brown Brown
Row 8: Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Brown Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Blue Brown Brown Blue Blue Blue Brown
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Blue Brown Brown Brown Blue Brown Blue
Row 12: Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Brown Blue
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Brown Pink Pink Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 23: Pink Pink Pink Brown Brown Brown Pink Pink Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 24: Pink Pink Brown Pink Brown Pink Brown Brown Brown Pink Brown Brown Brown Brown Pink Brown Pink Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 25: Pink Pink Brown Brown Pink Brown Brown Pink Brown Brown Pink Brown Pink Pink Brown Brown Pink Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 26: Pink Pink Brown Pink Brown Pink Brown Brown Brown Pink Brown Pink Pink Brown Pink Pink Pink Brown Brown Brown Brown Blue Blue Blue Blue Blue Brown Blue
Row 27: Brown Pink Brown Pink Brown Pink Pink Pink Pink Pink Brown Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 28: Brown Pink Pink Pink Pink Pink Brown Pink Pink Brown Brown Pink Brown Brown Pink Pink Pink Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Row 29: Brown Pink Brown Pink Pink Pink Brown Pink Pink Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Brown Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Brown Pink Pink
Row 2: Pink Pink Pink Brown Brown Brown Pink Pink Brown Pink Brown Brown Brown Brown Brown Pink Brown
Row 3: Pink Pink Brown Pink Brown Pink Brown Brown Brown Pink Brown Brown Brown Brown Pink Brown Pink
Row 4: Pink Pink Brown Brown Pink Brown Brown Pink Brown Brown Pink Brown Pink Pink Brown Brown Pink
Row 5: Pink Pink Brown Pink Brown Pink Brown Brown Brown Pink Brown Pink Pink Brown Pink Pink Pink
Row 6: Brown Pink Brown Pink Brown Pink Pink Pink Pink Pink Brown Pink Pink Brown Brown Brown Brown
Row 7: Brown Pink Pink Pink Pink Pink Brown Pink Pink Brown Brown Pink Brown Brown Pink Pink Pink
Row 8: Brown Pink Brown Pink Pink Pink Brown Pink Pink Brown Brown Brown Brown Brown Pink Pink Pink
Example 3
Input:
Row 1: Black Black Pink Black Pink Black Black Pink Pink Pink Pink Pink Red Pink Pink Red
Row 2: Black Black Pink Black Black Black Black Pink Pink Pink Pink Pink Red Pink Red Red
Row 3: Black Pink Black Black Pink Pink Black Pink Pink Pink Pink Pink Red Red Red Red
Row 4: Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Pink Red Red Red
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Red Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Red Red Red Pink
Row 11: Pink Pink Pink Red Pink Pink Red Pink Pink Pink Pink Pink Red Red Red Pink
Row 12: Red Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Red Red Red Red
Output:
Row 1: Black Black Pink Black Pink Black Black
Row 2: Black Black Pink Black Black Black Black
Row 3: Black Pink Black Black Pink Pink Black
Row 4: Black Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Orange Red Orange Red Red Red Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Orange Orange Orange Orange
Row 2: Red Red Red Orange Orange Red Red Orange Red Red Red Red Red Red Red Red Red Red Red Red Orange Orange Orange Orange Orange
Row 3: Red Red Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Orange Orange Orange Orange
Row 4: Orange Red Red Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Orange Orange Orange Orange
Row 5: Red Orange Red Orange Orange Red Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Orange Orange Red Orange
Row 6: Red Orange Orange Orange Red Red Orange Orange Red Red Red Red Red Red Red Red Red Red Red Red Orange Orange Orange Orange Orange
Row 7: Orange Red Orange Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Orange Orange Red Orange
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Orange Orange Red Orange
Row 10: Gray Gray Red Gray Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Orange Orange
Row 11: Gray Gray Red Red Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red
Row 12: Gray Gray Gray Gray Gray Red Red Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Orange Red
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Gray Gray Gray Gray Gray Gray Red
Gray Gray Red Gray Gray Gray Gray Gray
Gray Gray Red Red Gray Gray Gray Gray
Gray Gray Gray Gray Gray Red Red Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Black Pink
Row 2: Pink Black Black Black Pink Black Black Black Pink Black Black Black Pink Black Pink Black Black Black Pink Black Pink Black Pink Black Pink Black Pink
Row 3: Pink Black Pink Black Pink Pink Pink Black Pink Black Pink Black Pink Pink Pink Black Pink Pink Pink Black Pink Pink Pink Black Pink Pink Pink
Row 4: Pink Black Pink Black Black Black Pink Black Pink Black Pink Black Black Black Black Black Pink Black Black Black Black Black Black Black Black Black Pink
Row 5: Pink Pink Pink Black Pink Black Pink Black Pink Pink Pink Pink Pink Pink Pink Black Pink Black Pink Pink Pink Pink Pink Black Pink Pink Pink
Row 6: Black Black Pink Black Pink Black Pink Black Black Black Black Black Black Black Pink Black Pink Black Pink Black Black Black Pink Black Pink Black Black
Row 7: Pink Black Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Black Pink Black Pink Black Pink Pink Pink Black Pink Black Pink Black Pink
Row 8: Pink Black Pink Black Black Black Black Black Pink Black Black Black Black Black Pink Black Pink Black Black Black Pink Black Pink Black Pink Black Pink
Row 9: Pink Black Pink Black Pink Pink Pink Black Pink Black Pink Pink Pink Pink Pink Black Pink Pink Pink Black Pink Black Pink Black Pink Pink Pink
Row 10: Pink Black Pink Black Pink Black Pink Black Pink Black Pink Black Black Black Black Black Pink Black Pink Black Pink Black Pink Black Black Black Pink
Row 11: Pink Pink Pink Black Pink Black Pink Pink Pink Black Pink Pink Pink Black Pink Pink Pink Black Pink Black Pink Black Pink Black Pink Pink Pink
Row 12: Pink Black Black Black Pink Black Black Black Pink Black Black Black Pink Black Pink Black Black Black Black Black Pink Black Pink Black Black Black Pink
Row 13: Pink Pink Pink Black Pink Black Pink Black Pink Black Pink Pink Pink Black Pink Black Pink Pink Pink Black Pink Black Pink Pink Pink Black Pink
Row 14: Black Black Black Black Pink Black Pink Black Pink Black Pink Black Black Black Pink Black Pink Black Pink Black Pink Black Black Black Pink Black Pink
Row 15: Pink Pink Pink Pink Pink Black Pink Pink Pink Black Pink Black Pink Black Pink Pink Pink Black Pink Pink Pink Black Pink Pink Pink Black Pink
Row 16: Pink Black Black Black Pink Orange Gray Orange Black Black Pink Black Pink Black Black Black Black Black Pink Black Black Black Pink Black Black Black Pink
Row 17: Pink Pink Pink Black Pink Black Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Black Pink Black Pink Pink Pink Black Pink Pink Pink
Row 18: Pink Black Pink Black Black Black Pink Black Black Black Black Black Black Black Pink Black Pink Black Pink Black Pink Black Black Black Black Black Pink
Row 19: Pink Black Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Black Pink Black Pink Black Pink Pink Pink Pink Pink Black Pink
Row 20: Pink Black Black Black Black Black Black Black Pink Black Black Black Black Black Black Black Pink Black Black Black Black Black Black Black Pink Black Pink
Row 21: Pink Pink Pink Pink Pink Black Pink Pink Pink Black Pink Pink Pink Pink Pink Black Pink Black Pink Pink Pink Pink Pink Black Pink Black Pink
Row 22: Black Black Black Black Black Black Pink Black Black Black Pink Black Black Black Black Black Pink Black Pink Black Black Black Pink Black Pink Black Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Black Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Black Pink
Row 2: Pink Black Black Black Pink Orange Gray Orange Pink Black Black Black Pink Black Pink Black Black Black Pink Black Pink Black Pink Black Pink Black Pink
Row 3: Pink Black Pink Black Pink Pink Pink Gray Pink Black Pink Black Pink Pink Pink Black Pink Pink Pink Black Pink Pink Pink Black Pink Pink Pink
Row 4: Pink Black Pink Black Black Black Pink Orange Pink Black Pink Black Black Black Black Black Pink Black Black Black Black Black Black Black Black Black Pink
Row 5: Pink Pink Pink Black Pink Black Pink Gray Pink Pink Pink Pink Pink Pink Pink Black Pink Black Pink Pink Pink Pink Pink Black Pink Pink Pink
Row 6: Black Black Pink Black Pink Black Pink Orange Gray Orange Gray Orange Gray Orange Pink Black Pink Black Pink Black Black Black Pink Black Pink Black Black
Row 7: Pink Black Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Gray Pink Black Pink Black Pink Pink Pink Black Pink Black Pink Black Pink
Row 8: Pink Black Pink Black Black Black Black Black Pink Orange Gray Orange Gray Orange Pink Black Pink Black Black Black Pink Black Pink Black Pink Black Pink
Row 9: Pink Black Pink Black Pink Pink Pink Black Pink Gray Pink Pink Pink Pink Pink Black Pink Pink Pink Black Pink Black Pink Black Pink Pink Pink
Row 10: Pink Black Pink Black Pink Orange Pink Black Pink Orange Pink Black Black Black Black Black Pink Black Pink Black Pink Black Pink Black Black Black Pink
Row 11: Pink Pink Pink Black Pink Gray Pink Pink Pink Gray Pink Pink Pink Black Pink Pink Pink Black Pink Black Pink Black Pink Black Pink Pink Pink
Row 12: Pink Black Black Black Pink Orange Gray Orange Pink Orange Gray Orange Pink Black Pink Black Black Black Black Black Pink Black Pink Black Black Black Pink
Row 13: Pink Pink Pink Black Pink Gray Pink Gray Pink Gray Pink Pink Pink Black Pink Black Pink Pink Pink Black Pink Black Pink Pink Pink Black Pink
Row 14: Black Black Black Black Pink Orange Pink Orange Pink Orange Pink Black Black Black Pink Black Pink Black Pink Black Pink Black Black Black Pink Black Pink
Row 15: Pink Pink Pink Pink Pink Gray Pink Pink Pink Gray Pink Black Pink Black Pink Pink Pink Black Pink Pink Pink Black Pink Pink Pink Black Pink
Row 16: Pink Orange Gray Orange Pink Orange Gray Orange Gray Orange Pink Black Pink Black Black Black Black Black Pink Black Black Black Pink Black Black Black Pink
Row 17: Pink Pink Pink Gray Pink Gray Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Black Pink Black Pink Pink Pink Black Pink Pink Pink
Row 18: Pink Black Pink Orange Gray Orange Pink Black Black Black Black Black Black Black Pink Black Pink Black Pink Black Pink Black Black Black Black Black Pink
Row 19: Pink Black Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Black Pink Black Pink Black Pink Pink Pink Pink Pink Black Pink
Row 20: Pink Black Black Black Black Black Black Black Pink Black Black Black Black Black Black Black Pink Black Black Black Black Black Black Black Pink Black Pink
Row 21: Pink Pink Pink Pink Pink Black Pink Pink Pink Black Pink Pink Pink Pink Pink Black Pink Black Pink Pink Pink Pink Pink Black Pink Black Pink
Row 22: Black Black Black Black Black Black Pink Black Black Black Pink Black Black Black Black Black Pink Black Pink Black Black Black Pink Black Pink Black Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Black Pink
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Black Brown Orange Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 2: Brown Orange Orange Orange Brown Orange Brown Orange Orange Orange Brown Red Brown Orange Brown Orange Orange Orange Brown Orange Brown Orange Brown Orange Orange Orange Brown
Row 3: Brown Orange Brown Orange Brown Orange Brown Orange Brown Brown Brown Black Brown Brown Brown Brown Brown Orange Brown Orange Brown Orange Brown Orange Brown Brown Brown
Row 4: Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Orange Orange Brown Orange Orange Orange Orange Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown
Row 5: Brown Orange Brown Brown Brown Orange Brown Orange Brown Brown Brown Orange Brown Brown Brown Orange Brown Brown Brown Orange Brown Orange Brown Orange Brown Orange Brown
Row 6: Brown Orange Brown Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Orange Brown Orange Brown Orange Orange Orange Brown Orange Brown Orange Brown Orange Orange
Row 7: Brown Orange Brown Brown Brown Brown Brown Orange Brown Orange Brown Orange Brown Brown Brown Orange Brown Orange Brown Brown Brown Orange Brown Orange Brown Brown Brown
Row 8: Brown Orange Orange Orange Orange Orange Orange Orange Brown Orange Brown Orange Orange Orange Orange Orange Brown Orange Brown Orange Orange Orange Orange Orange Orange Orange Brown
Row 9: Brown Orange Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Orange Brown Brown Brown
Row 10: Brown Orange Brown Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Brown Orange Brown
Row 11: Brown Orange Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown
Output:
Row 1: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Black Brown Orange Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 2: Brown Orange Orange Orange Brown Orange Brown Orange Orange Orange Brown Red Brown Orange Brown Red Black Red Brown Orange Brown Orange Brown Orange Orange Orange Brown
Row 3: Brown Orange Brown Orange Brown Orange Brown Orange Brown Brown Brown Black Brown Brown Brown Brown Brown Black Brown Orange Brown Orange Brown Orange Brown Brown Brown
Row 4: Brown Orange Brown Orange Brown Orange Brown Orange Brown Red Black Red Brown Red Black Red Black Red Brown Orange Brown Orange Brown Orange Brown Orange Brown
Row 5: Brown Orange Brown Brown Brown Orange Brown Orange Brown Brown Brown Black Brown Brown Brown Black Brown Brown Brown Orange Brown Orange Brown Orange Brown Orange Brown
Row 6: Brown Orange Brown Orange Orange Orange Brown Orange Orange Orange Brown Red Black Red Brown Red Brown Orange Orange Orange Brown Orange Brown Orange Brown Orange Orange
Row 7: Brown Orange Brown Brown Brown Brown Brown Orange Brown Orange Brown Black Brown Brown Brown Black Brown Orange Brown Brown Brown Orange Brown Orange Brown Brown Brown
Row 8: Brown Orange Orange Orange Orange Orange Orange Orange Brown Orange Brown Red Black Red Black Red Brown Orange Brown Orange Orange Orange Orange Orange Orange Orange Brown
Row 9: Brown Orange Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Orange Brown Brown Brown
Row 10: Brown Orange Brown Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Brown Orange Brown
Row 11: Brown Orange Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown
Example 3
Input:
Row 1: Black Black Black Black Black Gray Black Black Black Black Black
Row 2: Gray Gray Black Gray Black Gray Black Gray Gray Gray Black
Row 3: Black Black Black Gray Black Black Black Gray Black Black Black
Row 4: Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Black Black Black Gray Black Black Black Black Black Black Black
Row 6: Black Gray Black Gray Black Gray Gray Brown Yellow Brown Black
Row 7: Black Gray Black Black Black Black Black Black Black Gray Black
Output:
Row 1: Black Black Black Black Black Gray Black Black Black Black Black
Row 2: Gray Gray Black Gray Black Gray Black Gray Gray Gray Black
Row 3: Black Black Black Gray Black Black Black Gray Black Black Black
Row 4: Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Black Black Black Gray Black Black Black Black Black Black Black
Row 6: Black Gray Black Gray Black Brown Yellow Brown Yellow Brown Black
Row 7: Black Gray Black Black Black Black Black Black Black Yellow Black
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Black Black Black Black Black Purple
Row 3: Purple Yellow Purple Purple Purple Black Purple
Row 4: Purple Gray Purple Black Purple Black Purple
Row 5: Purple Yellow Purple Black Purple Purple Purple
Row 6: Black Black Purple Black Black Black Purple
Row 7: Purple Purple Purple Black Purple Purple Purple
Row 8: Purple Black Black Black Black Black Purple
Row 9: Purple Purple Purple Purple Purple Black Purple
Row 10: Purple Black Black Black Purple Black Purple
Row 11: Purple Black Purple Black Purple Black Purple
Row 12: Purple Black Purple Black Purple Black Purple
Row 13: Purple Purple Purple Black Purple Black Purple
Row 14: Black Black Purple Black Purple Black Purple
Row 15: Purple Black Purple Black Purple Black Purple
Row 16: Purple Black Purple Black Purple Black Black
Row 17: Purple Black Purple Black Purple Purple Purple
Row 18: Purple Black Purple Black Black Black Purple
Row 19: Purple Purple Purple Black Purple Purple Purple
Row 20: Purple Black Black Black Purple Black Black
Row 21: Purple Purple Purple Black Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Purple
Purple Gray Yellow Gray Yellow Gray Purple
Purple Yellow Purple Purple Purple Yellow Purple
Purple Gray Purple Black Purple Gray Purple
Purple Yellow Purple Black Purple Purple Purple
Yellow Gray Purple Black Black Black Purple
Purple Purple Purple Black Purple Purple Purple
Purple Black Black Black Black Black Purple
Purple Purple Purple Purple Purple Black Purple
Purple Black Black Black Purple Black Purple
Purple Black Purple Black Purple Black Purple
Purple Black Purple Black Purple Black Purple
Purple Purple Purple Black Purple Black Purple
Black Black Purple Black Purple Black Purple
Purple Black Purple Black Purple Black Purple
Purple Black Purple Black Purple Black Black
Purple Black Purple Black Purple Purple Purple
Purple Black Purple Black Black Black Purple
Purple Purple Purple Black Purple Purple Purple
Purple Black Black Black Purple Black Black
Purple Purple Purple Black Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Black Black Black Gray Gray Gray Gray Gray Gray Brown Brown
Row 9: Brown Black Black Black Brown Brown Brown Gray Gray Gray Brown Brown
Row 10: Brown Black Black Black Brown Brown Brown Gray Gray Gray Brown Brown
Row 11: Brown Black Black Black Brown Brown Brown Gray Gray Gray Brown Brown
Row 12: Brown Black Black Black Brown Brown Brown Gray Gray Gray Brown Brown
Row 13: Brown Black Black Black Brown Brown Brown Gray Gray Gray Brown Brown
Row 14: Brown Black Black Black Brown Brown Brown Gray Gray Gray Brown Brown
Row 15: Brown Black Black Black Brown Brown Brown Gray Gray Gray Brown Brown
Row 16: Brown Black Black Black Brown Brown Brown Gray Gray Gray Brown Brown
Row 17: Brown Black Black Black Brown Brown Brown Gray Gray Gray Brown Brown
Row 18: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 27: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 28: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Black Black Black Gray Gray Gray Brown Brown Brown Brown Brown
Row 9: Brown Black Black Black Gray Gray Gray Brown Brown Brown Brown Brown
Row 10: Brown Black Black Black Gray Gray Gray Brown Brown Brown Brown Brown
Row 11: Brown Black Black Black Gray Gray Gray Brown Brown Brown Brown Brown
Row 12: Brown Black Black Black Gray Gray Gray Brown Brown Brown Brown Brown
Row 13: Brown Black Black Black Gray Gray Gray Brown Brown Brown Brown Brown
Row 14: Brown Black Black Black Gray Gray Gray Brown Brown Brown Brown Brown
Row 15: Brown Black Black Black Gray Gray Gray Brown Brown Brown Brown Brown
Row 16: Brown Black Black Black Gray Gray Gray Brown Brown Brown Brown Brown
Row 17: Brown Black Black Black Gray Gray Gray Brown Brown Brown Brown Brown
Row 18: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 27: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 28: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Pink Pink Pink
Row 27: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Pink Pink Pink
Row 28: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Pink Pink Pink
Row 29: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Pink Pink Pink
Row 27: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 28: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 29: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Example 3
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Gray Gray Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Yellow Gray Gray Gray Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Yellow Gray Gray Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Yellow Gray Gray Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Gray Gray Gray Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Gray Gray Gray Gray Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Gray Gray Gray Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Row 28: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Gray Gray Gray Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Gray Gray Gray Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Gray Gray Gray Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange Black Blue Orange Black Pink
Row 2: Orange Green Orange Orange Orange Red Blue
Row 3: Orange Orange Black Green Red Red Pink
Row 4: Orange Black Purple Orange Green Red Orange
Row 5: Orange Purple Blue Orange Orange Orange Red
Row 6: Orange Orange Black Orange Green Black Orange
Output:
Row 1: Orange Orange Gray Gray Orange Gray Gray
Row 2: Orange Gray Orange Orange Orange Gray Gray
Row 3: Orange Orange Gray Gray Gray Gray Gray
Row 4: Orange Gray Gray Orange Gray Gray Orange
Row 5: Orange Gray Gray Orange Orange Orange Gray
Row 6: Orange Orange Gray Orange Gray Gray Orange
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Yellow Black Black Black Black Black Black Black
Row 2: Black Black Red Black Black Black Blue Black Black Black Black Black Black Black Black
Row 3: Black Red Black Black Black Black Black Black Black Black Pink Black Black Black Red
Row 4: Red Black Orange Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Green Black Red Red Green Black Black Black Black Black Brown Black
Row 6: Orange Black Blue Black Black Blue Black Black Black Black Black Orange Black Black Yellow
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Orange Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Orange Yellow Orange
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Red Black Black Black Black Black Black Black Blue Black Orange
Row 11: Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black
Row 12: Black Green Black Black Black Black Black Black Black Black Black Black Black Brown Black
Row 13: Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Red Black Black Black Black Blue Black Pink
Row 15: Black Orange Black Black Black Black Green Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Blue Black Black Black Black Black Black Brown Black Orange Black
Row 17: Black Black Black Black Black Black Black Green Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Orange Black Black Black Red Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Yellow Black
Row 20: Black Green Black Black Black Black Black Black Black Black Black Red Black Black Black
Row 21: Black Black Black Black Red Black Black Black Black Yellow Red Green Blue Black Black
Row 22: Black Black Black Green Black Pink Blue Black Black Black Black Black Brown Black Black
Row 23: Black Black Black Black Green Black Orange Black Black Pink Orange Black Black Black Black
Row 24: Black Yellow Black Black Black Black Black Black Green Black Black Black Black Black Black
Row 25: Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black
Row 2: Black Black Gray Black Black Black Gray Black Black Black Black Black Black Black Black
Row 3: Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Gray
Row 4: Gray Black Gray Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Gray Black Gray Gray Gray Black Black Black Black Black Gray Black
Row 6: Gray Black Gray Black Black Gray Black Black Black Black Black Gray Black Black Gray
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Gray Gray Gray
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Gray Black Black Black Black Black Black Black Gray Black Gray
Row 11: Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black
Row 12: Black Gray Black Black Black Black Black Black Black Black Black Black Black Gray Black
Row 13: Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Gray Black Black Black Black Gray Black Gray
Row 15: Black Gray Black Black Black Black Gray Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Gray Black Black Black Black Black Black Gray Black Gray Black
Row 17: Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Gray Black Black Black Gray Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black
Row 20: Black Gray Black Black Black Black Black Black Black Black Black Gray Black Black Black
Row 21: Black Black Black Black Gray Black Black Black Black Gray Gray Gray Gray Black Black
Row 22: Black Black Black Gray Black Gray Gray Black Black Black Black Black Gray Black Black
Row 23: Black Black Black Black Gray Black Gray Black Black Gray Gray Black Black Black Black
Row 24: Black Gray Black Black Black Black Black Black Gray Black Black Black Black Black Black
Row 25: Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black
Example 3
Input:
Row 1: Red Red Red Red Red Green Red Red Orange Red Red Brown Brown Red Red Red Red Red Red Green
Row 2: Green Red Red Red Orange Red Pink Black Red Red Red Pink Red Red Red Pink Red Red Red Red
Row 3: Black Orange Red Red Blue Red Brown Red Red Orange Red Red Red Red Red Pink Red Red Red Red
Row 4: Black Red Red Red Red Brown Brown Red Red Red Red Red Pink Green Red Red Brown Orange Brown Red
Row 5: Orange Red Red Red Red Orange Red Red Red Red Red Purple Red Red Red Red Red Red Green Red
Row 6: Pink Red Red Red Blue Red Brown Red Red Black Red Pink Red Red Red Red Red Red Red Red
Row 7: Blue Red Red Red Red Green Red Purple Red Red Red Red Red Purple Red Red Purple Red Black Red
Row 8: Brown Red Black Red Red Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Purple Red Red Blue Brown Red Red Purple Red Red Red Red Red Red Purple Red Red Red Red
Row 10: Black Pink Pink Red Brown Red Red Blue Red Red Purple Blue Blue Purple Green Red Green Red Red Red
Row 11: Red Red Brown Red Purple Red Red Red Brown Red Red Red Purple Red Red Blue Orange Red Red Red
Row 12: Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Pink Green Red Red Green Red
Row 13: Red Red Purple Red Red Red Red Red Red Red Red Green Blue Red Black Orange Black Red Red Red
Output:
Row 1: Red Red Red Red Red Gray Red Red Gray Red Red Gray Gray Red Red Red Red Red Red Gray
Row 2: Gray Red Red Red Gray Red Gray Gray Red Red Red Gray Red Red Red Gray Red Red Red Red
Row 3: Gray Gray Red Red Gray Red Gray Red Red Gray Red Red Red Red Red Gray Red Red Red Red
Row 4: Gray Red Red Red Red Gray Gray Red Red Red Red Red Gray Gray Red Red Gray Gray Gray Red
Row 5: Gray Red Red Red Red Gray Red Red Red Red Red Gray Red Red Red Red Red Red Gray Red
Row 6: Gray Red Red Red Gray Red Gray Red Red Gray Red Gray Red Red Red Red Red Red Red Red
Row 7: Gray Red Red Red Red Gray Red Gray Red Red Red Red Red Gray Red Red Gray Red Gray Red
Row 8: Gray Red Gray Red Red Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Gray Red Red Gray Gray Red Red Gray Red Red Red Red Red Red Gray Red Red Red Red
Row 10: Gray Gray Gray Red Gray Red Red Gray Red Red Gray Gray Gray Gray Gray Red Gray Red Red Red
Row 11: Red Red Gray Red Gray Red Red Red Gray Red Red Red Gray Red Red Gray Gray Red Red Red
Row 12: Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Gray Gray Red Red Gray Red
Row 13: Red Red Gray Red Red Red Red Red Red Red Red Gray Gray Red Gray Gray Gray Red Red Red
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Brown Yellow Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Brown Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple
Row 8: Purple Yellow Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Green Orange Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Green Purple Purple Pink Purple Purple Purple Purple
Row 15: Purple Red Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple
Row 18: Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Gray Gray Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Gray Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple
Purple Gray Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Gray Purple Purple Gray Purple Purple Purple Purple
Purple Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple
Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Gray
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Red
Row 4: Red Blue Red Red Red Red Red Red Black Red Red Red Red Red Black Black Red Red Red Red Red Red Red Red Red Red Blue Red
Row 5: Red Blue Red Black Red Red Black Red Red Red Red Red Red Black Red Red Red Red Red Black Red Red Red Black Red Red Blue Red
Row 6: Red Blue Red Black Red Red Red Black Red Red Red Red Red Red Black Red Red Red Red Red Black Red Red Black Red Red Blue Red
Row 7: Red Blue Red Red Black Red Red Red Red Red Red Red Red Red Red Red Red Red Black Red Red Red Red Red Red Red Blue Red
Row 8: Red Blue Red Red Red Red Red Red Red Red Red Red Black Red Red Red Red Red Red Black Red Red Red Red Red Red Blue Red
Row 9: Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Black Red Red Red Red Red Red Red Red Red Red Red Blue Red
Row 10: Red Blue Red Red Black Red Red Black Red Red Red Red Red Red Red Red Red Red Red Red Red Black Black Red Red Red Blue Red
Row 11: Red Blue Red Red Red Red Red Red Red Black Red Red Red Red Red Red Red Red Red Red Red Black Red Red Red Red Blue Red
Row 12: Red Blue Red Red Red Red Black Red Red Red Red Red Red Black Red Red Red Red Red Red Black Red Red Red Red Red Blue Red
Row 13: Red Blue Red Red Red Red Black Red Red Red Red Black Red Red Red Red Black Red Red Red Red Red Red Red Red Red Blue Red
Row 14: Red Blue Red Black Red Red Red Red Red Red Red Black Red Red Red Red Red Red Black Black Red Red Red Red Black Red Blue Red
Row 15: Red Blue Red Red Red Black Black Red Red Red Red Red Black Red Red Red Red Red Red Black Red Red Black Red Red Red Blue Red
Row 16: Red Blue Red Red Red Red Black Red Red Black Red Red Red Black Red Red Red Black Red Red Red Red Red Red Red Red Blue Red
Row 17: Red Blue Red Red Red Red Red Red Black Red Red Red Red Red Black Red Red Red Red Red Red Black Red Red Red Red Blue Red
Row 18: Red Blue Black Red Red Black Red Red Black Red Red Red Red Red Red Red Red Red Red Red Black Red Red Red Red Red Blue Red
Row 19: Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Black Red Red Black Red Black Red Red Red Red Red Red Blue Red
Row 20: Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black Red Red Red Black Blue Red
Row 21: Red Blue Red Red Red Red Red Black Red Black Red Red Red Black Red Black Red Red Red Red Red Red Red Red Red Red Blue Red
Row 22: Red Blue Red Red Black Red Red Red Red Red Black Red Black Black Red Red Red Red Red Red Black Red Red Red Black Red Blue Red
Row 23: Red Blue Black Red Black Red Red Red Red Red Red Red Red Red Black Red Black Red Red Red Black Red Black Red Red Red Blue Red
Row 24: Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black Red Black Red Black Red Black Blue Red
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 26: Green Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Purple
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Yellow Red Red Red Red Red Gray Gray Red Red Red Red Red Red Red Red Red Red
Row 3: Red Yellow Red Red Yellow Red Red Red Red Red Red Yellow Red Red Red Red Red Gray Red Red Red Gray Red Red
Row 4: Red Yellow Red Red Red Yellow Red Red Red Red Red Red Gray Red Red Red Red Red Gray Red Red Gray Red Red
Row 5: Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Gray Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Yellow Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Red Red Red
Row 9: Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Red
Row 10: Red Red Red Red Yellow Red Red Red Red Red Red Yellow Red Red Red Red Red Red Gray Red Red Red Red Red
Row 11: Red Red Red Red Yellow Red Red Red Red Yellow Red Red Red Red Gray Red Red Red Red Red Red Red Red Red
Row 12: Red Green Red Red Red Red Red Red Red Green Red Red Red Red Red Red Purple Purple Red Red Red Red Purple Red
Row 13: Red Red Red Green Green Red Red Red Red Red Green Red Red Red Red Red Red Purple Red Red Purple Red Red Red
Row 14: Red Red Red Red Green Red Red Green Red Red Red Green Red Red Red Purple Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Green Red Red Red Red Red Purple Red Red Red Red Red Red Purple Red Red Red Red
Row 16: Green Red Red Green Red Red Green Red Red Red Red Red Red Red Red Red Red Red Purple Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Purple Red Red Purple Red Purple Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Purple Red Red Red Purple
Row 19: Red Red Red Red Red Green Red Green Red Red Red Green Red Purple Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Green Red Red Red Red Red Green Red Green Green Red Red Red Red Red Red Purple Red Red Red Purple Red
Row 21: Green Red Green Red Red Red Red Red Red Red Red Red Purple Red Purple Red Red Red Purple Red Purple Red Red Red
Row 22: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Purple Red Purple Red Purple Red Purple
Example 2
Input:
Row 1: Pink Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Orange
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Blue Red Blue Blue Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Blue Yellow Yellow Yellow Yellow Blue Blue Red Blue
Row 4: Blue Red Blue Blue Blue Yellow Blue Blue Blue Blue Yellow Yellow Blue Blue Yellow Yellow Blue Yellow Blue Blue Red Blue
Row 5: Blue Red Blue Blue Yellow Blue Yellow Blue Blue Yellow Blue Yellow Yellow Blue Blue Yellow Yellow Blue Blue Yellow Red Blue
Row 6: Blue Red Blue Yellow Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Yellow Blue Yellow Blue Blue Yellow Red Blue
Row 7: Blue Red Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Blue Yellow Red Blue
Row 8: Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Yellow Yellow Yellow Blue Blue Yellow Yellow Blue Red Blue
Row 9: Blue Red Blue Blue Yellow Yellow Blue Blue Yellow Blue Blue Yellow Blue Yellow Yellow Blue Blue Blue Blue Blue Red Blue
Row 10: Blue Red Blue Blue Blue Blue Yellow Yellow Blue Blue Blue Yellow Blue Blue Yellow Yellow Yellow Yellow Blue Blue Red Blue
Row 11: Blue Red Blue Blue Yellow Yellow Yellow Blue Blue Yellow Blue Yellow Yellow Yellow Yellow Blue Blue Blue Yellow Yellow Red Blue
Row 12: Blue Red Blue Blue Yellow Blue Blue Blue Blue Blue Blue Yellow Blue Blue Yellow Yellow Blue Yellow Yellow Yellow Red Blue
Row 13: Blue Red Blue Blue Blue Yellow Blue Yellow Yellow Yellow Blue Blue Yellow Yellow Blue Blue Blue Yellow Yellow Yellow Red Blue
Row 14: Blue Red Blue Blue Blue Blue Blue Yellow Yellow Blue Yellow Blue Blue Blue Yellow Blue Yellow Blue Yellow Blue Red Blue
Row 15: Blue Red Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Blue Yellow Blue Blue Blue Yellow Red Blue
Row 16: Blue Red Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Blue Blue Blue Yellow Yellow Blue Blue Blue Red Blue
Row 17: Blue Red Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Yellow Blue Yellow Red Blue
Row 18: Blue Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Yellow Blue Red Blue
Row 19: Blue Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Blue Blue Blue Blue Blue Blue Red Blue
Row 20: Blue Red Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow Yellow Blue Red Blue
Row 21: Blue Red Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Blue Yellow Blue Blue Yellow Yellow Blue Yellow Blue Red Blue
Row 22: Blue Red Blue Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Blue Blue Blue Blue Blue Blue Blue Red Blue
Row 23: Blue Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Yellow Blue Yellow Blue Yellow Blue Blue Red Blue
Row 24: Blue Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Blue Blue Blue Yellow Blue Yellow Blue Red Blue
Row 25: Blue Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Yellow Blue Blue Blue Blue Yellow Red Blue
Row 26: Blue Red Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Blue Blue Blue Yellow Red Blue
Row 27: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 28: Black Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Purple
Output:
Row 1: Blue Blue Blue Pink Blue Pink Blue Pink Blue Orange Blue Blue Orange Orange Orange Orange Blue Blue
Row 2: Blue Blue Blue Pink Blue Blue Blue Blue Pink Orange Blue Blue Orange Orange Blue Orange Blue Blue
Row 3: Blue Blue Pink Blue Pink Blue Blue Pink Blue Orange Orange Blue Blue Orange Orange Blue Blue Orange
Row 4: Blue Pink Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Orange Blue Orange Blue Blue Orange
Row 5: Pink Pink Pink Pink Pink Blue Pink Pink Pink Orange Blue Orange Orange Orange Orange Blue Blue Orange
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Orange Orange Orange Blue Blue Orange Orange Blue
Row 7: Blue Blue Pink Pink Blue Blue Pink Blue Blue Orange Blue Orange Orange Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Pink Pink Blue Blue Blue Orange Blue Blue Orange Orange Orange Orange Blue Blue
Row 9: Blue Blue Pink Pink Pink Blue Blue Pink Blue Orange Orange Orange Orange Blue Blue Blue Orange Orange
Row 10: Blue Blue Pink Blue Blue Blue Blue Blue Blue Orange Blue Blue Orange Orange Blue Orange Orange Orange
Row 11: Blue Blue Blue Pink Blue Pink Pink Pink Blue Blue Orange Orange Blue Blue Blue Orange Orange Orange
Row 12: Blue Blue Blue Blue Blue Pink Pink Blue Pink Blue Blue Blue Orange Blue Orange Blue Orange Blue
Row 13: Black Black Blue Black Black Black Black Black Black Blue Purple Purple Blue Purple Blue Blue Blue Purple
Row 14: Black Black Black Black Blue Black Black Black Black Blue Blue Blue Blue Purple Purple Blue Blue Blue
Row 15: Blue Black Black Black Black Blue Black Black Black Purple Purple Blue Blue Blue Blue Purple Blue Purple
Row 16: Black Black Black Black Black Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 17: Black Black Black Black Black Black Black Black Black Blue Purple Purple Blue Blue Blue Blue Blue Blue
Row 18: Black Black Black Black Black Black Blue Black Black Blue Blue Blue Blue Purple Purple Purple Purple Blue
Row 19: Black Black Black Black Black Blue Black Black Black Blue Purple Blue Blue Purple Purple Blue Purple Blue
Row 20: Blue Black Black Black Blue Black Black Black Black Blue Purple Blue Blue Blue Blue Blue Blue Blue
Row 21: Black Black Black Black Black Black Black Black Black Blue Blue Purple Blue Purple Blue Purple Blue Blue
Row 22: Black Black Black Black Black Black Black Black Black Blue Purple Blue Blue Blue Purple Blue Purple Blue
Row 23: Black Black Black Black Black Black Black Black Black Blue Blue Blue Purple Blue Blue Blue Blue Purple
Row 24: Black Black Black Black Blue Black Black Black Black Purple Purple Purple Blue Purple Blue Blue Blue Purple
Example 3
Input:
Row 1: Black Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red Brown
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Green Red Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Green
Row 4: Green Red Green Green Pink Pink Green Pink Pink Pink Pink Pink Green Pink Pink Pink Red Green
Row 5: Green Red Pink Green Green Pink Green Pink Pink Pink Pink Pink Pink Pink Green Pink Red Green
Row 6: Green Red Pink Pink Pink Green Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Red Green
Row 7: Green Red Green Green Green Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Green
Row 8: Green Red Green Green Pink Green Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Red Green
Row 9: Green Red Pink Green Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Red Green
Row 10: Green Red Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Green
Row 11: Green Red Pink Green Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Green
Row 12: Green Red Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Red Green
Row 13: Green Red Green Green Green Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Red Green
Row 14: Green Red Pink Green Green Green Pink Green Green Pink Green Pink Pink Pink Pink Green Red Green
Row 15: Green Red Green Pink Green Green Green Green Green Pink Pink Pink Green Pink Green Pink Red Green
Row 16: Green Red Green Green Pink Pink Pink Green Pink Pink Pink Pink Pink Green Pink Pink Red Green
Row 17: Green Red Green Green Green Pink Green Green Pink Pink Pink Green Pink Pink Pink Pink Red Green
Row 18: Green Red Green Pink Green Green Green Green Green Pink Pink Green Pink Green Pink Green Red Green
Row 19: Green Red Pink Green Green Green Green Green Green Pink Pink Green Pink Green Green Pink Red Green
Row 20: Green Red Green Green Pink Green Pink Pink Pink Pink Pink Pink Green Pink Green Green Red Green
Row 21: Green Red Pink Green Green Pink Green Pink Pink Pink Pink Green Green Green Pink Pink Red Green
Row 22: Green Red Pink Green Green Green Green Green Green Pink Pink Green Pink Pink Pink Pink Red Green
Row 23: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 24: Orange Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red Purple
Output:
Row 1: Green Green Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown
Row 2: Green Green Black Black Green Black Black Brown Brown Brown Green Brown Brown Brown
Row 3: Black Green Green Black Green Black Black Brown Brown Brown Brown Brown Green Brown
Row 4: Black Black Black Green Black Black Black Brown Brown Green Brown Brown Brown Brown
Row 5: Green Green Green Black Green Black Black Brown Brown Brown Brown Brown Brown Brown
Row 6: Green Green Black Green Black Green Black Brown Brown Brown Brown Brown Brown Brown
Row 7: Black Green Black Black Black Black Green Brown Brown Brown Brown Brown Brown Brown
Row 8: Black Green Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown
Row 9: Black Green Black Black Green Black Black Brown Brown Brown Brown Brown Brown Brown
Row 10: Black Black Black Green Black Black Black Brown Brown Brown Brown Brown Brown Green
Row 11: Green Green Green Orange Orange Orange Orange Purple Green Purple Purple Purple Purple Purple
Row 12: Orange Green Green Green Orange Green Green Purple Green Purple Purple Purple Purple Green
Row 13: Green Orange Green Green Green Green Green Purple Purple Purple Green Purple Green Purple
Row 14: Green Green Orange Orange Orange Green Orange Purple Purple Purple Purple Green Purple Purple
Row 15: Green Green Green Orange Green Green Orange Purple Purple Green Purple Purple Purple Purple
Row 16: Green Orange Green Green Green Green Green Purple Purple Green Purple Green Purple Green
Row 17: Orange Green Green Green Green Green Green Purple Purple Green Purple Green Green Purple
Row 18: Green Green Orange Green Orange Orange Orange Purple Purple Purple Green Purple Green Green
Row 19: Orange Green Green Orange Green Orange Orange Purple Purple Green Green Green Purple Purple
Row 20: Orange Green Green Green Green Green Green Purple Purple Green Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Purple Gray Yellow Yellow Gray Black
Row 2: Gray Gray Gray Gray Gray Gray
Row 3: Yellow Gray Yellow Yellow Gray Yellow
Row 4: Yellow Gray Yellow Yellow Gray Yellow
Row 5: Yellow Gray Yellow Pink Gray Yellow
Row 6: Yellow Gray Pink Pink Gray Yellow
Row 7: Yellow Gray Pink Yellow Gray Yellow
Row 8: Yellow Gray Yellow Yellow Gray Yellow
Row 9: Yellow Gray Yellow Yellow Gray Yellow
Row 10: Yellow Gray Pink Pink Gray Yellow
Row 11: Yellow Gray Yellow Yellow Gray Yellow
Row 12: Yellow Gray Pink Yellow Gray Yellow
Row 13: Yellow Gray Yellow Pink Gray Yellow
Row 14: Yellow Gray Pink Yellow Gray Yellow
Row 15: Yellow Gray Yellow Yellow Gray Yellow
Row 16: Yellow Gray Yellow Yellow Gray Yellow
Row 17: Yellow Gray Yellow Pink Gray Yellow
Row 18: Yellow Gray Yellow Yellow Gray Yellow
Row 19: Yellow Gray Pink Yellow Gray Yellow
Row 20: Yellow Gray Pink Yellow Gray Yellow
Row 21: Yellow Gray Pink Yellow Gray Yellow
Row 22: Yellow Gray Yellow Pink Gray Yellow
Row 23: Yellow Gray Pink Yellow Gray Yellow
Row 24: Yellow Gray Pink Yellow Gray Yellow
Row 25: Gray Gray Gray Gray Gray Gray
Row 26: Brown Gray Yellow Yellow Gray Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Yellow Yellow
Yellow Yellow
Yellow Black
Purple Black
Purple Yellow
Yellow Yellow
Yellow Yellow
Purple Black
Yellow Yellow
Purple Yellow
Yellow Black
Brown Yellow
Yellow Yellow
Yellow Yellow
Yellow Orange
Yellow Yellow
Brown Yellow
Brown Yellow
Brown Yellow
Yellow Orange
Brown Yellow
Brown Yellow |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Purple Purple Purple Pink Pink Pink Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Purple Purple Purple Pink Pink Pink Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Purple Purple Purple Pink Pink Pink Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Purple Purple Purple Pink Pink Pink Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 27: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Purple Pink Pink Purple Pink Pink Purple Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Purple Pink Pink Purple Pink Pink Purple Pink
Row 5: Purple Purple Purple Pink Pink Pink Pink Pink Pink
Row 6: Purple Purple Purple Purple Pink Pink Purple Pink Pink
Row 7: Purple Purple Purple Pink Pink Pink Pink Pink Pink
Row 8: Purple Purple Purple Pink Purple Pink Pink Purple Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Purple Pink Pink Purple Pink Pink Purple Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Purple Pink Pink Purple Pink Pink Purple Pink
Row 13: Pink Pink Pink Purple Purple Purple Pink Pink Pink
Row 14: Purple Pink Pink Purple Purple Purple Purple Pink Pink
Row 15: Pink Pink Pink Purple Purple Purple Pink Pink Pink
Row 16: Pink Purple Pink Purple Purple Purple Pink Purple Pink
Example 2
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow
Row 4: Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow
Row 5: Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow
Row 6: Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow
Row 7: Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow
Row 14: Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow
Row 15: Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow
Row 16: Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow
Row 17: Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow
Row 28: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 29: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 30: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Pink
Row 2: Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow
Row 3: Pink Yellow Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Pink Pink
Row 4: Yellow Yellow Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Yellow
Row 5: Yellow Pink Yellow Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Pink
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Pink Pink Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Pink Yellow Yellow Yellow Yellow Yellow
Row 11: Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Pink
Row 12: Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Pink Yellow
Row 13: Pink Yellow Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Pink Pink Pink Yellow Pink Pink Pink Pink Yellow Pink Pink Pink
Row 14: Yellow Yellow Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Pink Pink Yellow
Row 15: Yellow Pink Yellow Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Pink Yellow Pink Yellow Pink Pink Yellow Pink Yellow Pink Pink
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Pink Pink Pink Yellow Pink Pink Pink Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Pink Yellow Pink Yellow Pink Pink Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Pink
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Pink Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Pink Pink Pink Yellow Pink Pink Pink
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Pink Pink Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Pink Yellow Pink Yellow Pink Pink
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Green Green Green Green Green Green Brown Brown Brown Brown Brown
Row 4: Brown Brown Green Green Green Green Green Green Brown Brown Brown Brown Brown
Row 5: Brown Brown Green Green Green Green Green Green Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Green Green Green Brown Brown Brown Green Green Green Brown Brown
Row 10: Brown Brown Green Green Green Brown Brown Brown Green Green Green Brown Brown
Row 11: Brown Brown Green Green Green Brown Brown Brown Green Green Green Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Green Green Brown Green Green Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Green Brown Green Green Brown Green Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Green Green Brown Brown Brown Brown Green Green Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Green Brown Green Brown Brown Brown Green Brown Green
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 3: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 4: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 5: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 6: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 7: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 8: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 9: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 10: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 11: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 12: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 22: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 23: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 24: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 25: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 26: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange
Row 27: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Orange Orange Green Green Orange Orange Green Green Orange Orange Green Green Orange Orange
Orange Green Green Green Orange Green Green Green Orange Green Green Green Orange Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Orange Orange Green Green Orange Orange Green Green Orange Orange Green Green Orange Orange
Orange Green Green Green Orange Green Green Green Orange Green Green Green Orange Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange
Green Green Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange
Green Green Orange Orange Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Green Green Green Orange Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange
Green Green Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green
Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green
Orange Orange Orange Orange Green Green Orange Orange Green Green Orange Orange Green Green Orange Orange
Orange Orange Orange Orange Orange Green Green Green Orange Green Green Green Orange Green Green Green
Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Orange Orange Green Green Orange Orange Green Green Orange Orange Green Green Orange Orange
Orange Green Green Green Orange Green Green Green Orange Green Green Green Orange Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Purple Purple Purple Purple Purple Purple Black Gray Black Gray Black Gray Black Gray Black Gray Black Gray
Row 2: Black Black Black Black Black Black Purple Gray Black Gray Black Gray Black Gray Black Gray Black Black
Row 3: Purple Purple Purple Purple Purple Black Purple Black Black Gray Black Gray Black Gray Black Gray Gray Gray
Row 4: Black Black Black Black Purple Black Purple Black Purple Gray Black Gray Black Gray Black Black Black Black
Row 5: Purple Purple Purple Black Purple Black Purple Black Purple Black Black Gray Black Gray Gray Gray Gray Gray
Row 6: Black Black Purple Black Purple Black Purple Black Purple Black Purple Gray Black Black Black Black Black Black
Row 7: Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Gray Gray Gray Gray Gray Gray
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow
Output:
Row 1: Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue
Row 2: Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Brown
Row 3: Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Blue Blue
Row 4: Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Brown Brown Brown
Row 5: Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Blue Blue Blue Blue
Row 6: Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Brown Brown Brown Brown Brown
Row 7: Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Blue Blue Blue Blue Blue Blue
Row 8: Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Brown Brown Brown Brown Brown
Row 13: Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Yellow Yellow Yellow Yellow
Row 14: Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Brown Brown Brown
Row 15: Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Yellow Yellow
Row 16: Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Brown
Row 17: Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow
Example 3
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink
Output:
Row 1: Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown
Row 2: Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Orange
Row 3: Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Brown Brown
Row 4: Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Orange Orange Orange
Row 5: Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Brown Brown Brown Brown
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Pink Pink Pink Pink
Row 8: Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Orange Orange Orange
Row 9: Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Pink Pink
Row 10: Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Orange
Row 11: Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink
Here is the input grid for the test example:
Input:
Row 1: Black Gray Gray Gray Gray Gray Blue
Row 2: Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray
Row 24: Gray Gray Gray Gray Gray Gray Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Gray Black Gray Blue Gray Blue
Gray Gray Black Gray Blue Gray Gray
Black Black Black Gray Blue Blue Blue
Gray Gray Gray Gray Gray Gray Gray
Black Black Black Gray Blue Blue Blue
Gray Gray Gray Gray Gray Gray Gray
Black Black Black Gray Blue Blue Blue
Gray Gray Gray Gray Gray Gray Gray
Black Black Black Gray Blue Blue Blue
Gray Gray Gray Gray Gray Gray Gray
Black Black Black Gray Blue Blue Blue
Gray Gray Gray Gray Gray Gray Gray
Black Black Black Gray Blue Blue Blue
Gray Gray Gray Gray Gray Gray Gray
Black Black Black Gray Blue Blue Blue
Gray Gray Gray Gray Gray Gray Gray
Black Black Black Gray Blue Blue Blue
Gray Gray Gray Gray Gray Gray Gray
Black Black Black Gray Blue Blue Blue
Gray Gray Gray Gray Gray Gray Gray
Black Black Black Gray Blue Blue Blue
Gray Gray Gray Gray Gray Gray Gray
Black Black Black Gray Blue Blue Blue
Gray Gray Gray Gray Gray Gray Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Orange Orange Orange Orange
Row 2: Orange Orange Yellow Orange Yellow Orange Black Black Orange Orange Yellow Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Yellow Yellow Yellow Orange Orange Black Orange Orange Yellow Yellow Yellow Orange Orange Gray Orange Orange Purple Purple Purple Orange Orange Orange Orange Green
Row 4: Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Purple Orange Purple Orange Green Green Green Green
Row 5: Black Black Black Black Black Black Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange Orange
Row 6: Black Orange Orange Orange Orange Black Orange Black Orange Orange Black Orange Orange Orange Orange Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange
Row 7: Black Orange Orange Orange Orange Black Orange Orange Orange Orange Black Black Black Black Black Orange Orange Orange Orange Gray Orange Black Black Black Orange Orange
Row 8: Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Black Orange Orange Green Green
Row 10: Orange Orange Black Black Orange Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Orange Black Orange Orange Orange Green
Row 11: Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Yellow Yellow Orange Black Orange Orange Green Green
Row 12: Orange Orange Orange Black Orange Orange Black Orange Orange Orange Green Green Green Orange Orange Orange Green Orange Orange Yellow Orange Black Orange Orange Orange Orange
Row 13: Orange Orange Orange Black Orange Orange Black Orange Orange Orange Green Orange Orange Orange Orange Orange Green Orange Orange Yellow Orange Orange Orange Black Orange Black
Row 14: Orange Orange Orange Black Orange Orange Black Black Orange Green Green Green Orange Orange Orange Orange Green Green Green Orange Orange Orange Orange Black Black Black
Output:
Row 1: Orange Orange Pink Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange
Row 2: Orange Orange Pink Orange Pink Orange Blue Blue Orange Orange Blue Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Pink Pink Pink Orange Orange Blue Orange Orange Blue Blue Blue Orange Orange Blue Orange Orange Pink Pink Pink Orange Orange Orange Orange Blue
Row 4: Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Blue Blue Blue Orange Orange Pink Orange Pink Orange Blue Blue Blue Blue
Row 5: Pink Pink Pink Pink Pink Pink Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange
Row 6: Pink Orange Orange Orange Orange Pink Orange Blue Orange Orange Red Orange Orange Orange Orange Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange
Row 7: Pink Orange Orange Orange Orange Pink Orange Orange Orange Orange Red Red Red Red Red Orange Orange Orange Orange Blue Orange Blue Blue Blue Orange Orange
Row 8: Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Blue Orange Orange Pink Pink
Row 10: Orange Orange Blue Blue Orange Orange Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Orange Blue Orange Orange Orange Pink
Row 11: Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Blue Blue Orange Blue Orange Orange Pink Pink
Row 12: Orange Orange Orange Blue Orange Orange Blue Orange Orange Orange Red Red Red Orange Orange Orange Pink Orange Orange Blue Orange Blue Orange Orange Orange Orange
Row 13: Orange Orange Orange Blue Orange Orange Blue Orange Orange Orange Red Orange Orange Orange Orange Orange Pink Orange Orange Blue Orange Orange Orange Pink Orange Pink
Row 14: Orange Orange Orange Blue Orange Orange Blue Blue Orange Red Red Red Orange Orange Orange Orange Pink Pink Pink Orange Orange Orange Orange Pink Pink Pink
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple
Row 2: Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Orange Orange Orange Orange Orange Purple
Row 3: Orange Orange Orange Orange Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Green Orange Orange Orange Orange Orange Purple
Row 4: Gray Orange Orange Orange Orange Gray Orange Gray Orange Orange Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Brown Brown Orange Orange Purple
Row 5: Gray Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Gray Orange Orange Orange Orange Green Green Green Orange Orange Brown Orange Orange Orange Purple
Row 6: Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Black Orange Green Orange Orange Orange Orange Brown Orange Orange Orange Purple
Row 7: Gray Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Black Orange Green Green Green Orange Orange Brown Orange Orange Orange Orange
Row 8: Gray Orange Orange Gray Orange Green Green Green Orange Orange Gray Gray Gray Orange Orange Black Orange Orange Orange Orange Orange Brown Brown Brown Orange Green Green
Row 9: Gray Orange Orange Gray Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Green
Row 10: Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Black Black Black Black Black Black Orange Brown Brown Orange Orange Green
Row 11: Orange Green Green Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Black Orange Brown Orange Orange Green Green
Row 12: Orange Green Orange Orange Gray Orange Green Green Green Orange Orange Brown Orange Green Orange Green Orange Black Black Orange Black Orange Brown Brown Orange Orange Orange
Row 13: Orange Green Orange Orange Gray Orange Orange Orange Orange Orange Orange Brown Orange Green Orange Green Orange Black Orange Orange Black Orange Orange Orange Orange Orange Orange
Row 14: Orange Green Green Orange Gray Orange Orange Orange Orange Brown Orange Brown Orange Green Orange Green Orange Black Orange Orange Orange Yellow Orange Orange Yellow Orange Orange
Row 15: Orange Orange Orange Orange Gray Orange Gray Gray Orange Brown Brown Brown Orange Green Green Green Orange Black Black Black Orange Yellow Yellow Yellow Yellow Orange Brown
Row 16: Gray Gray Gray Gray Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Brown
Row 17: Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Orange Orange Orange Orange Brown
Row 18: Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Brown
Row 19: Yellow Yellow Yellow Orange Orange Orange Gray Gray Orange Orange Orange Orange Yellow Orange Orange Orange Brown Orange Yellow Yellow Orange Green Orange Brown Brown Brown Brown
Row 20: Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Brown Orange Orange Yellow Orange Green Orange Brown Orange Orange Brown
Row 21: Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Brown Brown Orange Yellow Orange Orange Orange Brown Orange Orange Orange
Row 22: Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Yellow Orange Orange Orange Brown Orange Orange Orange
Row 23: Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Black Black Orange Black Orange Orange Orange Orange Orange Orange Orange Yellow Orange Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Black Orange
Row 26: Orange Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Orange Black Black Black Black Black Black Orange
Row 27: Orange Purple Orange Orange Black Orange Orange Orange Black Orange Orange Orange Gray Orange Orange Orange Brown Orange Brown Orange Orange Orange Orange Orange Orange Black Orange
Row 28: Orange Purple Orange Orange Orange Orange Purple Orange Orange Orange Orange Orange Gray Orange Gray Orange Brown Orange Brown Orange Yellow Yellow Yellow Yellow Orange Orange Orange
Row 29: Orange Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue
Row 2: Orange Orange Orange Orange Orange Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Orange Orange Orange Orange Orange Blue
Row 3: Orange Orange Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Pink Orange Orange Orange Orange Orange Blue
Row 4: Red Orange Orange Orange Orange Pink Orange Pink Orange Orange Red Red Red Red Red Red Orange Orange Orange Orange Orange Orange Red Red Orange Orange Blue
Row 5: Red Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Red Orange Orange Orange Orange Pink Pink Pink Orange Orange Red Orange Orange Orange Blue
Row 6: Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Red Orange Pink Orange Orange Orange Orange Red Orange Orange Orange Blue
Row 7: Red Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Red Orange Pink Pink Pink Orange Orange Red Orange Orange Orange Orange
Row 8: Red Orange Orange Red Orange Red Red Red Orange Orange Red Red Red Orange Orange Red Orange Orange Orange Orange Orange Red Red Red Orange Pink Pink
Row 9: Red Orange Orange Red Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Pink
Row 10: Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Red Red Red Red Red Red Orange Pink Pink Orange Orange Pink
Row 11: Orange Pink Pink Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Red Orange Pink Orange Orange Pink Pink
Row 12: Orange Pink Orange Orange Blue Orange Red Red Red Orange Orange Pink Orange Pink Orange Pink Orange Pink Pink Orange Red Orange Pink Pink Orange Orange Orange
Row 13: Orange Pink Orange Orange Blue Orange Orange Orange Orange Orange Orange Pink Orange Pink Orange Pink Orange Pink Orange Orange Red Orange Orange Orange Orange Orange Orange
Row 14: Orange Pink Pink Orange Blue Orange Orange Orange Orange Pink Orange Pink Orange Pink Orange Pink Orange Pink Orange Orange Orange Red Orange Orange Red Orange Orange
Row 15: Orange Orange Orange Orange Blue Orange Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Red Red Red Red Orange Red
Row 16: Blue Blue Blue Blue Blue Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Red
Row 17: Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Orange Orange Orange Orange Red
Row 18: Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange Red
Row 19: Blue Blue Blue Orange Orange Orange Pink Pink Orange Orange Orange Orange Red Orange Orange Orange Blue Orange Pink Pink Orange Blue Orange Red Red Red Red
Row 20: Orange Orange Blue Orange Orange Orange Orange Orange Red Red Red Red Red Orange Orange Orange Blue Orange Orange Pink Orange Blue Orange Red Orange Orange Red
Row 21: Orange Orange Blue Orange Orange Orange Orange Orange Red Orange Orange Orange Red Orange Orange Orange Blue Blue Orange Pink Orange Orange Orange Red Orange Orange Orange
Row 22: Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Pink Pink Orange Orange Orange Red Orange Orange Orange
Row 23: Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Blue Blue Orange Red Orange Orange Orange Orange Orange Orange Orange Red Orange Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Red Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Red Orange
Row 26: Orange Orange Orange Orange Red Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange Red Red Red Red Red Red Orange
Row 27: Orange Pink Orange Orange Red Orange Orange Orange Red Orange Orange Orange Pink Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange Orange Orange Red Orange
Row 28: Orange Pink Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Pink Orange Pink Orange Pink Orange Pink Orange Blue Blue Blue Blue Orange Orange Orange
Row 29: Orange Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange
Example 3
Input:
Row 1: Brown Yellow Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown
Row 2: Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Yellow Brown Brown Yellow Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Yellow Brown Brown Brown Brown Yellow
Row 4: Brown Purple Purple Brown Purple Purple Purple Brown Brown Brown Yellow Yellow Yellow Yellow Brown Brown Brown Brown Yellow
Row 5: Brown Purple Brown Brown Purple Brown Purple Brown Brown Brown Brown Brown Brown Yellow Brown Brown Yellow Yellow Yellow
Row 6: Brown Purple Brown Brown Purple Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Yellow
Row 7: Brown Purple Brown Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown
Row 8: Brown Purple Brown Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Purple Purple Purple Purple Brown Brown Purple Brown Brown Brown Brown Purple Brown Brown Yellow Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Brown Brown Yellow Brown Brown Brown
Row 11: Brown Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown
Row 12: Brown Purple Brown Brown Brown Brown Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Brown Yellow Yellow Yellow Brown
Row 13: Brown Purple Brown Purple Purple Brown Brown Brown Brown Yellow Brown Yellow Brown Brown Brown Yellow Brown Yellow Brown
Row 14: Brown Purple Brown Brown Purple Brown Brown Brown Brown Yellow Brown Yellow Brown Brown Brown Brown Brown Yellow Brown
Row 15: Brown Purple Brown Brown Purple Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown
Row 16: Yellow Brown Brown Brown Brown Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Brown Yellow Brown Brown
Row 17: Yellow Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Brown Brown
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Yellow Brown Purple Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Yellow Yellow Yellow Brown Purple Purple Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Pink Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown
Row 2: Brown Pink Pink Pink Pink Pink Brown Brown Brown Brown Red Brown Brown Red Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Red Brown Brown Brown Brown Red
Row 4: Brown Pink Pink Brown Pink Pink Pink Brown Brown Brown Red Red Red Red Brown Brown Brown Brown Red
Row 5: Brown Pink Brown Brown Pink Brown Pink Brown Brown Brown Brown Brown Brown Red Brown Brown Red Red Red
Row 6: Brown Pink Brown Brown Pink Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Red
Row 7: Brown Pink Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown
Row 8: Brown Pink Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Pink Pink Pink Pink Brown Brown Pink Brown Brown Brown Brown Pink Brown Brown Red Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Brown Brown Red Brown Brown Brown
Row 11: Brown Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown
Row 12: Brown Blue Brown Brown Brown Brown Brown Blue Blue Blue Brown Red Red Brown Brown Red Red Red Brown
Row 13: Brown Blue Brown Blue Blue Brown Brown Brown Brown Blue Brown Red Brown Brown Brown Red Brown Red Brown
Row 14: Brown Blue Brown Brown Blue Brown Brown Brown Brown Blue Brown Red Brown Brown Brown Brown Brown Red Brown
Row 15: Brown Blue Brown Brown Blue Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown
Row 16: Pink Brown Brown Brown Brown Pink Brown Red Red Red Red Red Red Brown Pink Brown Pink Brown Brown
Row 17: Pink Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown
Row 18: Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Red Red Red Brown Blue Blue Blue Blue Blue Blue Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Blue Brown Red Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Blue Blue Blue Brown Red Red Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Yellow Orange Orange Orange Orange
Row 2: Orange Yellow Yellow Yellow Yellow Orange Orange Orange Orange Brown Orange Orange Orange Yellow Orange Orange Orange Yellow
Row 3: Orange Orange Orange Orange Yellow Orange Orange Orange Orange Brown Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Brown Orange Orange Orange Orange Brown
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Brown Orange Brown Brown Brown Brown
Row 7: Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Brown Orange Brown Orange Orange Brown
Row 8: Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Brown Orange Brown Orange Orange Orange
Row 9: Yellow Orange Orange Orange Yellow Orange Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Yellow Orange Orange Orange Yellow Orange Brown Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Yellow Orange Orange Orange Orange Orange Brown Orange Orange Brown Orange Orange Green Green Green Orange Brown Orange
Row 12: Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Orange Green Orange Orange Orange Brown Brown
Row 13: Orange Green Orange Orange Yellow Orange Orange Yellow Orange Orange Brown Orange Green Orange Orange Orange Orange Orange
Row 14: Orange Green Orange Orange Yellow Orange Orange Yellow Orange Orange Brown Orange Green Green Green Orange Orange Orange
Row 15: Green Green Orange Orange Yellow Yellow Yellow Yellow Orange Orange Brown Brown Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Brown Orange Brown Orange Orange Orange Orange Orange Orange Yellow Orange Green Orange Orange Orange Green Orange Orange
Row 19: Orange Orange Brown Orange Orange Yellow Orange Orange Orange Yellow Orange Green Green Green Green Green Orange Orange
Row 20: Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Pink Orange Orange Orange Orange
Orange Blue Blue Blue Blue Orange Orange Orange Orange Red Orange Orange Orange Pink Orange Orange Orange Pink
Orange Orange Orange Orange Blue Orange Orange Orange Orange Red Orange Orange Orange Pink Pink Pink Pink Pink
Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Red Red Red Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Red Orange Orange Orange Orange Red
Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Red Orange Red Red Red Red
Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Red Orange Red Orange Orange Red
Pink Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Red Orange Red Orange Orange Orange
Pink Orange Orange Orange Pink Orange Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Pink Orange Orange Orange Pink Orange Pink Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange
Pink Orange Orange Orange Orange Orange Pink Orange Orange Pink Orange Orange Pink Pink Pink Orange Blue Orange
Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Blue Orange Pink Orange Orange Orange Blue Blue
Orange Blue Orange Orange Red Orange Orange Red Orange Orange Blue Orange Pink Orange Orange Orange Orange Orange
Orange Blue Orange Orange Red Orange Orange Red Orange Orange Blue Orange Pink Pink Pink Orange Orange Orange
Blue Blue Orange Orange Red Red Red Red Orange Orange Blue Blue Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Pink Orange Pink Orange Orange Orange Orange Orange Orange Blue Orange Pink Orange Orange Orange Pink Orange Orange
Orange Orange Pink Orange Orange Blue Orange Orange Orange Blue Orange Pink Pink Pink Pink Pink Orange Orange
Orange Orange Orange Orange Orange Blue Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange
Orange Blue Blue Blue Blue Blue Orange Orange Orange Blue Blue Blue Orange Orange Orange Orange Orange Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Yellow Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Yellow Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 21: Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red
Row 22: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Output:
Row 1: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Row 2: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Row 3: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Row 4: Red Blue Red Blue Red Red Yellow Red Blue Red Red Red Red Red
Row 5: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Row 6: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Row 7: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Row 8: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Row 9: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Row 10: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Row 11: Red Blue Red Blue Red Red Red Red Blue Yellow Red Red Red Red
Row 12: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Row 13: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Row 14: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Row 15: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Row 16: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Row 17: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Row 18: Red Blue Red Blue Red Red Red Red Blue Red Red Yellow Red Red
Row 19: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Row 20: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Row 21: Red Blue Red Blue Yellow Red Red Red Blue Red Red Red Red Red
Row 22: Red Blue Red Blue Red Red Red Red Blue Red Red Red Red Red
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 27: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink
Row 28: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Green Brown Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Green Pink Brown Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 20: Pink Pink Pink Green Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 27: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Green Pink
Row 28: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Example 3
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Gray Black Black Black Black Black Black Black Black Black
Row 4: Yellow Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Gray Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Yellow Black Black Black Black Black Black Black Black Gray Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Yellow Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Yellow Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Yellow Black Black Gray Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Yellow Black Black Black Gray Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Yellow Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 24: Yellow Black Black Black Black Black Black Black Black Black Black Black Black
Row 25: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 26: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 27: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 28: Black Black Black Black Black Black Black Black Black Black Gray Black Black
Row 29: Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Gray Black Black Black Black Black Black Black Black Black
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Gray Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Black Black Black
Row 10: Black Black Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Yellow Yellow Yellow Gray Black Black Black Black Black Black Black Black Black
Row 18: Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Yellow Yellow Yellow Yellow Gray Black Black Black Black Black Black Black Black
Row 21: Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 25: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 26: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 27: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 28: Black Black Black Black Black Black Black Black Black Black Gray Black Black
Row 29: Black Black Black Black Black Black Black Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Yellow Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Gray Red Black Black Black
Row 2: Black Black Black Black Black Orange Black
Row 3: Green Black Black Black Brown Black Black
Row 4: Black Black Red Red Black Black Black
Row 5: Brown Red Black Black Red Black Black
Row 6: Pink Brown Black Black Black Black Black
Row 7: Black Pink Black Black Black Black Black
Row 8: Pink Green Pink Black Black Yellow Black
Row 9: Black Black Pink Black Black Red Red
Row 10: Black Orange Pink Black Black Black Black
Row 11: Black Red Black Black Red Red Black
Row 12: Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Red Black
Row 14: Red Black Black Black Black Black Black
Row 15: Black Black Black Black Brown Black Black
Row 16: Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Red Gray
Row 18: Black Black Black Black Black Black Pink
Row 19: Black Green Black Pink Black Black Black
Row 20: Black Black Black Black Black Black Red
Row 21: Black Red Black Black Red Black Black
Row 22: Black Black Red Black Black Black Black
Row 23: Red Red Black Black Black Black Black
Row 24: Black Black Black Black Black Black Green
Output:
Row 1: Black Black Gray Red Black Black Black
Row 2: Black Black Black Black Black Blue Black
Row 3: Blue Black Black Black Blue Black Black
Row 4: Black Black Red Red Black Black Black
Row 5: Brown Red Black Black Blue Black Black
Row 6: Pink Brown Black Black Black Black Black
Row 7: Black Pink Black Black Black Black Black
Row 8: Pink Green Pink Black Black Yellow Black
Row 9: Black Black Pink Black Black Red Red
Row 10: Black Orange Pink Black Black Black Black
Row 11: Black Red Black Black Red Red Black
Row 12: Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Blue Black
Row 14: Blue Black Black Black Black Black Black
Row 15: Black Black Black Black Blue Black Black
Row 16: Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Red Gray
Row 18: Black Black Black Black Black Black Pink
Row 19: Black Blue Black Blue Black Black Black
Row 20: Black Black Black Black Black Black Blue
Row 21: Black Blue Black Black Blue Black Black
Row 22: Black Black Blue Black Black Black Black
Row 23: Red Red Black Black Black Black Black
Row 24: Black Black Black Black Black Black Blue
Example 2
Input:
Row 1: Black Black Black Black Black Black Gray Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black Black Black Black Black Purple Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Black Purple Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Gray Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Blue Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black
Example 3
Input:
Row 1: Purple Black Orange Orange Black Black Black
Row 2: Black Gray Black Black Black Black Black
Row 3: Black Green Black Black Black Black Black
Row 4: Black Purple Black Black Black Black Black
Row 5: Black Green Black Black Green Black Pink
Row 6: Black Black Purple Black Black Black Black
Row 7: Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Green
Row 9: Black Black Black Black Black Black Brown
Row 10: Green Black Black Black Black Black Pink
Row 11: Brown Black Black Black Black Yellow Black
Row 12: Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black
Row 14: Red Orange Black Black Black Black Yellow
Row 15: Black Black Black Purple Black Green Black
Row 16: Black Black Black Black Black Black Black
Row 17: Black Green Black Green Green Brown Black
Row 18: Black Black Black Black Black Black Black
Row 19: Orange Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Orange
Row 21: Yellow Black Black Black Black Black Black
Row 22: Brown Black Black Brown Black Black Black
Row 23: Black Black Black Black Black Black Black
Row 24: Black Orange Black Pink Black Black Black
Row 25: Black Black Black Black Black Black Black
Output:
Row 1: Blue Black Orange Orange Black Black Black
Row 2: Black Gray Black Black Black Black Black
Row 3: Black Green Black Black Black Black Black
Row 4: Black Purple Black Black Black Black Black
Row 5: Black Green Black Black Blue Black Blue
Row 6: Black Black Blue Black Black Black Black
Row 7: Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Green
Row 9: Black Black Black Black Black Black Brown
Row 10: Green Black Black Black Black Black Pink
Row 11: Brown Black Black Black Black Blue Black
Row 12: Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black
Row 14: Red Orange Black Black Black Black Blue
Row 15: Black Black Black Blue Black Blue Black
Row 16: Black Black Black Black Black Black Black
Row 17: Black Blue Black Green Green Brown Black
Row 18: Black Black Black Black Black Black Black
Row 19: Blue Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Blue
Row 21: Yellow Black Black Black Black Black Black
Row 22: Brown Black Black Blue Black Black Black
Row 23: Black Black Black Black Black Black Black
Row 24: Black Blue Black Blue Black Black Black
Row 25: Black Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Black Gray Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Orange Black Orange Black Black Black Black Brown
Row 2: Black Black Black Black Yellow Black Black Black Black Black Black Brown Black Black Brown Yellow Black Black Black Black Black Black Gray Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Brown Purple Black Black Black Black Black Black Black Pink Black Black Pink Black Black Black Black Black Black Black Black Brown
Row 6: Pink Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black Black Orange Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Black
Row 8: Black Black Yellow Black Black Black Black Black Brown Black Black Black Green Black Black Black Brown Black Brown Black Black Black Black Black
Row 9: Black Black Black Black Black Yellow Black Black Black Black Black Black Black Orange Yellow Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Brown Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Gray
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Purple Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Pink Black Black Black Black Black Black Black Black
Row 14: Brown Black Brown Black Black Black Black Black Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Yellow Black Black Black Black Brown Black Black Black Green Black Black Purple Black Yellow Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Brown Pink Black Brown Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Pink Orange Black Black Black Purple Black Black Brown
Row 18: Black Brown Black Black Purple Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Orange Black
Row 19: Orange Black Black Black Black Black Black Brown Black Black Black Brown Black Black Orange Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Yellow Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Brown Brown Black Black Black Black Black Black Black Black Black Pink Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Brown Pink Black Black Black Brown Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Gray Black Pink Black Black Black Brown Black Black Black Black Black Black Gray Black Black Black Black Black
Row 24: Black Black Brown Black Black Black Black Black Black Black Black Black Purple Black Black Brown Black Black Black Brown Black Black Black Black
Row 25: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black Black Black Black
Row 26: Black Black Black Purple Brown Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Blue Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Blue Black Blue Black Black Black Black Blue
Black Black Black Black Blue Black Black Black Black Black Black Blue Black Black Brown Yellow Black Black Black Black Black Black Blue Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Brown Purple Black Black Black Black Black Black Black Blue Black Black Blue Black Black Black Black Black Black Black Black Blue
Blue Black Black Black Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Blue Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Blue Black Black Black Black
Black Black Blue Black Black Black Black Black Blue Black Black Black Blue Black Black Black Blue Black Blue Black Black Black Black Black
Black Black Black Black Black Blue Black Black Black Black Black Black Black Orange Yellow Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Blue Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Blue
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Purple Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Pink Black Black Black Black Black Black Black Black
Blue Black Blue Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Blue Black Black Black Black Blue Black Black Black Green Black Black Blue Black Blue Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Brown Pink Black Blue Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Blue Black Black Pink Orange Black Black Black Blue Black Black Blue
Black Blue Black Black Blue Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Blue Black
Blue Black Black Black Black Black Black Blue Black Black Black Blue Black Black Blue Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Brown Brown Black Black Black Black Black Black Black Black Black Blue Black Black
Black Black Black Black Black Black Black Black Black Black Brown Pink Black Black Black Blue Black Black Black Black Black Black Black Black
Black Black Black Black Black Blue Black Blue Black Black Black Brown Black Black Black Black Black Black Blue Black Black Black Black Black
Black Black Blue Black Black Black Black Black Black Black Black Black Blue Black Black Brown Black Black Black Blue Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black Black Black Black
Black Black Black Purple Brown Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Green Pink Blue Pink
Row 2: Yellow Blue Pink Gray Green
Row 3: Pink Green Gray Pink Yellow
Output:
Row 1: Pink Green Pink Blue Pink Black Black Black Black Black Pink Green Pink Blue Pink Black Black Black Black Black Pink Green Pink Blue Pink
Row 2: Yellow Blue Pink Gray Green Black Black Black Black Black Yellow Blue Pink Gray Green Black Black Black Black Black Yellow Blue Pink Gray Green
Row 3: Pink Green Gray Pink Yellow Black Black Black Black Black Pink Green Gray Pink Yellow Black Black Black Black Black Pink Green Gray Pink Yellow
Row 4: Black Black Black Black Black Black Black Black Black Black Pink Green Pink Blue Pink Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Yellow Blue Pink Gray Green Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Pink Green Gray Pink Yellow Black Black Black Black Black Black Black Black Black Black
Row 7: Pink Green Pink Blue Pink Black Black Black Black Black Black Black Black Black Black Pink Green Pink Blue Pink Black Black Black Black Black
Row 8: Yellow Blue Pink Gray Green Black Black Black Black Black Black Black Black Black Black Yellow Blue Pink Gray Green Black Black Black Black Black
Row 9: Pink Green Gray Pink Yellow Black Black Black Black Black Black Black Black Black Black Pink Green Gray Pink Yellow Black Black Black Black Black
Example 2
Input:
Row 1: Brown Brown Blue
Row 2: Green Yellow Yellow
Row 3: Blue Blue Blue
Row 4: Pink Blue Gray
Row 5: Green Gray Blue
Output:
Row 1: Black Black Black Black Black Black Brown Brown Blue
Row 2: Black Black Black Black Black Black Green Yellow Yellow
Row 3: Black Black Black Black Black Black Blue Blue Blue
Row 4: Black Black Black Black Black Black Pink Blue Gray
Row 5: Black Black Black Black Black Black Green Gray Blue
Row 6: Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black
Row 11: Brown Brown Blue Brown Brown Blue Brown Brown Blue
Row 12: Green Yellow Yellow Green Yellow Yellow Green Yellow Yellow
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Pink Blue Gray Pink Blue Gray Pink Blue Gray
Row 15: Green Gray Blue Green Gray Blue Green Gray Blue
Row 16: Black Black Black Brown Brown Blue Black Black Black
Row 17: Black Black Black Green Yellow Yellow Black Black Black
Row 18: Black Black Black Blue Blue Blue Black Black Black
Row 19: Black Black Black Pink Blue Gray Black Black Black
Row 20: Black Black Black Green Gray Blue Black Black Black
Row 21: Black Black Black Black Black Black Brown Brown Blue
Row 22: Black Black Black Black Black Black Green Yellow Yellow
Row 23: Black Black Black Black Black Black Blue Blue Blue
Row 24: Black Black Black Black Black Black Pink Blue Gray
Row 25: Black Black Black Black Black Black Green Gray Blue
Example 3
Input:
Row 1: Blue Blue Yellow Blue
Row 2: Blue Blue Blue Blue
Row 3: Gray Blue Blue Blue
Row 4: Yellow Blue Gray Blue
Output:
Row 1: Blue Blue Yellow Blue Blue Blue Yellow Blue Black Black Black Black Blue Blue Yellow Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Black Blue Blue Blue Blue
Row 3: Gray Blue Blue Blue Gray Blue Blue Blue Black Black Black Black Gray Blue Blue Blue
Row 4: Yellow Blue Gray Blue Yellow Blue Gray Blue Black Black Black Black Yellow Blue Gray Blue
Row 5: Blue Blue Yellow Blue Blue Blue Yellow Blue Blue Blue Yellow Blue Blue Blue Yellow Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Gray Blue Blue Blue Gray Blue Blue Blue Gray Blue Blue Blue Gray Blue Blue Blue
Row 8: Yellow Blue Gray Blue Yellow Blue Gray Blue Yellow Blue Gray Blue Yellow Blue Gray Blue
Row 9: Black Black Black Black Blue Blue Yellow Blue Blue Blue Yellow Blue Blue Blue Yellow Blue
Row 10: Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Black Black Black Black Gray Blue Blue Blue Gray Blue Blue Blue Gray Blue Blue Blue
Row 12: Black Black Black Black Yellow Blue Gray Blue Yellow Blue Gray Blue Yellow Blue Gray Blue
Row 13: Black Black Black Black Blue Blue Yellow Blue Black Black Black Black Blue Blue Yellow Blue
Row 14: Black Black Black Black Blue Blue Blue Blue Black Black Black Black Blue Blue Blue Blue
Row 15: Black Black Black Black Gray Blue Blue Blue Black Black Black Black Gray Blue Blue Blue
Row 16: Black Black Black Black Yellow Blue Gray Blue Black Black Black Black Yellow Blue Gray Blue
Here is the input grid for the test example:
Input:
Row 1: Orange Yellow Red Brown Yellow
Row 2: Blue Orange Red Blue Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Yellow Red Brown Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Blue Orange Red Blue Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Orange Yellow Red Brown Yellow Black Black Black Black Black Black Black Black Black Black Orange Yellow Red Brown Yellow
Black Black Black Black Black Blue Orange Red Blue Orange Black Black Black Black Black Black Black Black Black Black Blue Orange Red Blue Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Blue Blue Blue Blue Blue Blue Yellow
Row 15: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Blue Blue Blue Blue Blue Blue Yellow
Row 16: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Blue Blue Blue Blue Blue Blue Yellow
Row 17: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Blue Blue Blue Blue Blue Blue Yellow
Row 18: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Blue Blue Blue Blue Blue Blue Yellow
Row 9: Yellow Blue Blue Blue Blue Blue Blue Yellow
Row 10: Yellow Blue Blue Blue Blue Blue Blue Yellow
Row 11: Yellow Blue Blue Blue Blue Blue Blue Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 2
Input:
Row 1: Green Green Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Orange Orange Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Orange Orange
Example 3
Input:
Row 1: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 2: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 3: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 4: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 5: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 6: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red
Row 10: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red
Row 11: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red
Row 12: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red
Row 13: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red
Row 14: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red
Row 15: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 16: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 17: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 18: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 19: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Output:
Row 1: Red Red Red
Row 2: Red Red Red
Row 3: Red Red Red
Row 4: Red Red Red
Row 5: Red Red Red
Row 6: Red Red Red
Row 7: Purple Purple Purple
Row 8: Purple Purple Purple
Row 9: Purple Purple Purple
Row 10: Purple Purple Purple
Row 11: Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Yellow Blue Pink
Row 2: Yellow Blue Pink
Row 3: Yellow Blue Pink
Row 4: Yellow Blue Pink
Row 5: Yellow Blue Pink
Row 6: Yellow Blue Pink
Row 7: Yellow Blue Pink
Row 8: Yellow Blue Pink
Row 9: Blue Blue Blue
Row 10: Blue Blue Blue
Row 11: Blue Blue Blue
Row 12: Blue Blue Blue
Row 13: Blue Blue Blue
Row 14: Pink Blue Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Yellow
Yellow
Yellow
Yellow
Yellow
Yellow
Yellow
Yellow |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Gray Orange Gray Yellow Purple Orange Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Yellow Gray Blue Purple Green Gray Green Brown Purple Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Blue Red Purple Green Blue Brown Red Gray Green Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Red Purple Yellow Orange Green Green Brown Green Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Red Gray Gray Red Red Yellow Brown Red Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Red Red Red Red Yellow Blue Brown Blue Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Yellow Yellow Gray Green Orange Blue Green Gray Brown Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Yellow Red Gray Blue Gray Red Blue Red Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Blue Blue Blue Blue Red Orange Red Purple Gray Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Orange Red Orange Purple Gray Brown Orange Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Gray Orange Gray Brown Gray Brown Green Gray Blue Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Gray Orange Gray Purple Brown Orange Brown Purple Gray Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Blue Brown Brown Red Green Blue Brown Brown Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Green Gray Purple Blue Green Orange Red Green Brown Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Yellow Purple Green Brown Green Purple Brown Blue Green Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Orange Gray Blue Brown Red Brown Brown Yellow Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Orange Brown Brown Purple Green Gray Brown Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Purple Green Blue Red Yellow Gray Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Brown Orange Purple Blue Gray Purple Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Blue Brown Red Orange Red Red Gray Yellow Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Brown Purple Purple Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Yellow Red Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Blue Gray Orange Gray Yellow Purple Orange Yellow Yellow Pink Pink Yellow Yellow Orange Purple Yellow Gray Orange Gray Blue
Row 2: Yellow Gray Blue Purple Green Gray Green Brown Purple Gray Gray Purple Brown Green Gray Green Purple Blue Gray Yellow
Row 3: Blue Red Purple Green Blue Brown Red Gray Green Orange Orange Green Gray Red Brown Blue Green Purple Red Blue
Row 4: Red Purple Yellow Orange Green Green Brown Green Red Pink Pink Red Green Brown Green Green Orange Yellow Purple Red
Row 5: Red Gray Gray Red Red Yellow Brown Red Yellow Yellow Yellow Yellow Red Brown Yellow Red Red Gray Gray Red
Row 6: Red Red Red Red Yellow Blue Brown Blue Brown Pink Pink Brown Blue Brown Blue Yellow Red Red Red Red
Row 7: Yellow Yellow Gray Green Orange Blue Green Gray Brown Orange Orange Brown Gray Green Blue Orange Green Gray Yellow Yellow
Row 8: Yellow Red Gray Blue Gray Red Blue Red Orange Pink Pink Orange Red Blue Red Gray Blue Gray Red Yellow
Row 9: Blue Blue Blue Blue Red Orange Red Purple Gray Yellow Yellow Gray Purple Red Orange Red Blue Blue Blue Blue
Row 10: Orange Red Orange Purple Gray Brown Orange Blue Blue Pink Pink Blue Blue Orange Brown Gray Purple Orange Red Orange
Row 11: Gray Orange Gray Brown Gray Brown Green Gray Blue Purple Purple Blue Gray Green Brown Gray Brown Gray Orange Gray
Row 12: Gray Orange Gray Purple Brown Orange Brown Purple Gray Orange Orange Gray Purple Brown Orange Brown Purple Gray Orange Gray
Row 13: Blue Brown Brown Red Green Blue Brown Brown Blue Pink Pink Blue Brown Brown Blue Green Red Brown Brown Blue
Row 14: Green Gray Purple Blue Green Orange Red Green Brown Red Red Brown Green Red Orange Green Blue Purple Gray Green
Row 15: Yellow Purple Green Brown Green Purple Brown Blue Green Brown Brown Green Blue Brown Purple Green Brown Green Purple Yellow
Row 16: Orange Gray Blue Brown Red Brown Brown Yellow Red Pink Pink Red Yellow Brown Brown Red Brown Blue Gray Orange
Row 17: Orange Brown Brown Purple Green Gray Brown Green Pink Pink Pink Pink Green Brown Gray Green Purple Brown Brown Orange
Row 18: Purple Green Blue Red Yellow Gray Blue Pink Pink Pink Pink Pink Pink Blue Gray Yellow Red Blue Green Purple
Row 19: Brown Orange Purple Blue Gray Purple Green Pink Pink Pink Pink Pink Pink Green Purple Gray Blue Purple Orange Brown
Row 20: Blue Brown Red Orange Red Red Gray Yellow Purple Pink Pink Purple Yellow Gray Red Red Orange Red Brown Blue
Row 21: Brown Purple Purple Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Purple Purple Brown
Row 22: Yellow Red Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Red Yellow
Row 23: Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red
Example 2
Input:
Row 1: Yellow Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Blue Yellow Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Gray Red Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Brown Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Yellow Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Yellow
Row 2: Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown
Row 3: Blue Yellow Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Yellow Blue
Row 4: Gray Red Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Red Gray
Row 5: Brown Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Brown
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Green Green
Row 5: Purple Purple Purple Purple Purple Purple Purple Orange Orange Blue
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Brown Green
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown
Row 9: Purple Purple Purple Purple Purple Purple Purple Red Orange Orange
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Red Pink
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Red
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Pink Purple Purple Purple Purple Purple Purple Purple Purple Pink
Row 2: Orange Orange Purple Purple Purple Purple Purple Purple Orange Orange
Row 3: Orange Purple Purple Purple Purple Purple Purple Purple Purple Orange
Row 4: Green Green Purple Purple Purple Purple Purple Purple Green Green
Row 5: Blue Orange Orange Purple Purple Purple Purple Orange Orange Blue
Row 6: Blue Purple Purple Purple Purple Purple Purple Purple Purple Blue
Row 7: Green Brown Purple Purple Purple Purple Purple Purple Brown Green
Row 8: Brown Purple Purple Purple Purple Purple Purple Purple Purple Brown
Row 9: Orange Orange Red Purple Purple Purple Purple Red Orange Orange
Row 10: Pink Red Purple Purple Purple Purple Purple Purple Red Pink
Row 11: Red Purple Purple Purple Purple Purple Purple Purple Purple Red
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Red Red Red
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Blue Blue Red
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red
Red Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red
Red Red Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red
Red Red Red Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Red Red Red
Red Blue Blue Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Blue Blue Red
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Orange Brown Brown Brown Brown Gray Gray Orange Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Gray Brown Brown Brown Brown Gray Gray Orange Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Gray Gray Brown
Row 7: Brown Brown Brown Gray Gray Gray Brown Brown Gray Gray Brown Brown Brown Brown Gray Gray Gray Gray Gray Brown
Row 8: Brown Brown Brown Gray Gray Gray Brown Brown Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Orange Gray Gray Brown Brown Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Gray Gray Gray Gray Gray Brown Brown Brown Brown Brown Gray Gray Orange Gray Gray Brown Brown Brown Brown
Row 12: Brown Gray Gray Gray Gray Gray Brown Brown Brown Brown Brown Gray Gray Gray Gray Gray Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Gray Gray Orange
Row 2: Gray Gray Orange
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Purple Purple
Row 6: Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple
Row 7: Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Purple Purple
Row 8: Pink Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple
Row 10: Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Purple Purple
Row 11: Pink Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Purple Purple
Row 12: Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Purple Purple
Row 14: Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple
Row 15: Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple
Row 16: Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange
Row 4: Pink Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange
Row 7: Pink Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange
Row 8: Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink
Row 10: Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue
Row 4: Yellow Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue
Row 5: Yellow Blue Brown Blue Blue Brown Blue Blue Brown Brown Blue Blue Blue Brown
Row 6: Yellow Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Blue Blue Blue Blue Blue Blue Brown Blue Blue Brown Brown Brown Blue Yellow
Row 10: Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Yellow
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue
Row 3: Blue Brown Blue Blue Brown Blue Blue Brown Brown Blue Blue Blue Brown
Row 4: Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Blue Brown Brown Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Brown Blue Blue Brown Blue Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Brown Brown Blue Blue Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Brown Blue Blue Blue Brown Brown Blue Blue Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Brown Blue Blue Brown Brown Brown Blue Blue Blue Blue Brown Blue Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Brown Blue Blue Blue Blue Blue Blue Brown Brown Brown Blue Blue Blue Brown Blue Blue Blue Blue Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Brown Brown Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Brown Blue Blue Brown Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Brown Brown Blue Blue
Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Brown Blue Blue Blue Brown Brown Blue Blue
Blue Blue Blue Blue Blue Blue Brown Blue Blue Brown Brown Brown Blue Blue Blue Blue Brown Blue
Brown Blue Blue Blue Blue Blue Blue Brown Brown Brown Blue Blue Blue Brown Blue Blue Blue Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Green Pink Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink
Row 12: Green Green Green Yellow Green Yellow Green Green Yellow Green Yellow Yellow Yellow Green Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Yellow Yellow Green
Row 13: Green Green Green Green Green Yellow Yellow Green Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Green Yellow Green Green Yellow Green Green Yellow Green Green
Row 14: Green Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green
Row 15: Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green
Row 16: Green Pink Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink
Row 17: Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 25: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 26: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 27: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 28: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Yellow Yellow Green Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Green Yellow Green Green Yellow Green Green Yellow Green Green
Row 8: Green Green Green Yellow Green Yellow Green Green Yellow Green Yellow Yellow Yellow Green Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Yellow Yellow Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Green Pink Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Pink Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink
Row 17: Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green
Row 20: Green Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 25: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 26: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 27: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 28: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Brown Brown Black Black Black Brown Brown Black Black
Row 4: Black Black Black Brown Black Purple Black Purple Black Brown Black Black
Row 5: Black Black Black Brown Black Black Black Purple Black Brown Black Black
Row 6: Black Black Black Brown Black Black Black Purple Black Brown Black Black
Row 7: Black Black Black Brown Black Black Black Purple Black Brown Black Black
Row 8: Black Black Black Brown Black Purple Black Black Black Brown Black Black
Row 9: Black Black Black Brown Black Black Black Purple Black Brown Black Black
Row 10: Black Black Black Brown Black Black Black Purple Black Brown Black Black
Row 11: Black Black Black Brown Black Purple Black Purple Black Brown Black Black
Row 12: Black Black Black Brown Black Black Black Purple Black Brown Black Black
Row 13: Black Black Black Brown Black Black Black Black Black Brown Black Black
Row 14: Black Black Black Brown Black Black Black Purple Black Brown Black Black
Row 15: Black Black Black Brown Black Purple Black Purple Black Brown Black Black
Row 16: Black Black Black Brown Black Black Black Purple Black Brown Black Black
Row 17: Black Black Black Brown Brown Black Black Black Brown Brown Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Brown Brown Black Black Black Brown Brown Black Black
Row 4: Black Purple Black Brown Black Black Black Black Black Brown Black Purple
Row 5: Black Black Black Brown Black Black Black Black Black Brown Black Purple
Row 6: Black Black Black Brown Black Black Black Black Black Brown Black Purple
Row 7: Black Black Black Brown Black Black Black Black Black Brown Black Purple
Row 8: Black Purple Black Brown Black Black Black Black Black Brown Black Black
Row 9: Black Black Black Brown Black Black Black Black Black Brown Black Purple
Row 10: Black Black Black Brown Black Black Black Black Black Brown Black Purple
Row 11: Black Purple Black Brown Black Black Black Black Black Brown Black Purple
Row 12: Black Black Black Brown Black Black Black Black Black Brown Black Purple
Row 13: Black Black Black Brown Black Black Black Black Black Brown Black Black
Row 14: Black Black Black Brown Black Black Black Black Black Brown Black Purple
Row 15: Black Purple Black Brown Black Black Black Black Black Brown Black Purple
Row 16: Black Black Black Brown Black Black Black Black Black Brown Black Purple
Row 17: Black Black Black Brown Brown Black Black Black Brown Brown Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black
Example 3
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Green Green Orange Orange Green Green Orange Orange Orange
Row 5: Orange Orange Orange Green Orange Purple Purple Orange Green Orange Orange Orange
Row 6: Orange Orange Orange Green Orange Purple Orange Orange Green Orange Orange Orange
Row 7: Orange Orange Orange Green Orange Purple Orange Orange Green Orange Orange Orange
Row 8: Orange Orange Orange Green Orange Orange Orange Orange Green Orange Orange Orange
Row 9: Orange Orange Orange Green Orange Purple Purple Orange Green Orange Orange Orange
Row 10: Orange Orange Orange Green Orange Orange Orange Orange Green Orange Orange Orange
Row 11: Orange Orange Orange Green Green Orange Orange Green Green Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Green Green Orange Orange Green Green Orange Orange Orange
Row 5: Orange Purple Orange Green Orange Orange Orange Orange Green Orange Purple Orange
Row 6: Orange Purple Orange Green Orange Orange Orange Orange Green Orange Orange Orange
Row 7: Orange Purple Orange Green Orange Orange Orange Orange Green Orange Orange Orange
Row 8: Orange Orange Orange Green Orange Orange Orange Orange Green Orange Orange Orange
Row 9: Orange Purple Orange Green Orange Orange Orange Orange Green Orange Purple Orange
Row 10: Orange Orange Orange Green Orange Orange Orange Orange Green Orange Orange Orange
Row 11: Orange Orange Orange Green Green Orange Orange Green Green Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Pink Pink Gray Gray Gray Gray Pink Pink Gray Gray Gray Gray
Row 4: Gray Gray Gray Pink Gray Blue Gray Gray Blue Gray Pink Gray Gray Gray Gray
Row 5: Gray Gray Gray Pink Gray Blue Gray Gray Blue Gray Pink Gray Gray Gray Gray
Row 6: Gray Gray Gray Pink Gray Blue Gray Gray Blue Gray Pink Gray Gray Gray Gray
Row 7: Gray Gray Gray Pink Gray Blue Gray Gray Gray Gray Pink Gray Gray Gray Gray
Row 8: Gray Gray Gray Pink Gray Blue Gray Gray Blue Gray Pink Gray Gray Gray Gray
Row 9: Gray Gray Gray Pink Gray Blue Gray Gray Blue Gray Pink Gray Gray Gray Gray
Row 10: Gray Gray Gray Pink Gray Blue Gray Gray Blue Gray Pink Gray Gray Gray Gray
Row 11: Gray Gray Gray Pink Gray Blue Gray Gray Blue Gray Pink Gray Gray Gray Gray
Row 12: Gray Gray Gray Pink Gray Gray Gray Gray Blue Gray Pink Gray Gray Gray Gray
Row 13: Gray Gray Gray Pink Pink Gray Gray Gray Gray Pink Pink Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Pink Pink Gray Gray Gray Gray Pink Pink Gray Gray Gray Gray
Gray Blue Gray Pink Gray Gray Gray Gray Gray Gray Pink Gray Blue Gray Gray
Gray Blue Gray Pink Gray Gray Gray Gray Gray Gray Pink Gray Blue Gray Gray
Gray Blue Gray Pink Gray Gray Gray Gray Gray Gray Pink Gray Blue Gray Gray
Gray Blue Gray Pink Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray
Gray Blue Gray Pink Gray Gray Gray Gray Gray Gray Pink Gray Blue Gray Gray
Gray Blue Gray Pink Gray Gray Gray Gray Gray Gray Pink Gray Blue Gray Gray
Gray Blue Gray Pink Gray Gray Gray Gray Gray Gray Pink Gray Blue Gray Gray
Gray Blue Gray Pink Gray Gray Gray Gray Gray Gray Pink Gray Blue Gray Gray
Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Pink Gray Blue Gray Gray
Gray Gray Gray Pink Pink Gray Gray Gray Gray Pink Pink Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red
Row 26: Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown
Row 27: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Gray Gray Gray Gray Brown Brown Red Brown Brown Brown
Row 2: Brown Gray Gray Gray Gray Brown Brown Gray Brown Gray Gray
Row 3: Brown Red Gray Brown Brown Gray Gray Gray Brown Gray Brown
Row 4: Brown Gray Red Brown Brown Gray Brown Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Brown Gray Brown Brown Gray
Row 6: Gray Gray Gray Gray Brown Gray Gray Gray Brown Brown Red
Row 7: Gray Gray Gray Gray Brown Gray Brown Brown Brown Brown Gray
Row 8: Gray Gray Brown Gray Gray Gray Brown Brown Gray Gray Gray
Row 9: Gray Gray Brown Gray Brown Brown Brown Brown Gray Gray Gray
Row 10: Brown Brown Brown Red Brown Brown Gray Gray Gray Gray Brown
Row 11: Brown Brown Brown Gray Brown Brown Gray Gray Gray Gray Brown
Row 12: Brown Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown
Row 13: Brown Gray Brown Brown Gray Brown Brown Red Brown Gray Gray
Row 14: Gray Gray Gray Gray Gray Brown Brown Gray Brown Gray Brown
Row 15: Brown Brown Gray Brown Brown Gray Gray Gray Brown Red Brown
Row 16: Gray Gray Gray Brown Brown Gray Brown Brown Brown Gray Brown
Row 17: Gray Brown Brown Gray Gray Gray Brown Gray Gray Gray Brown
Row 18: Gray Brown Brown Gray Brown Brown Brown Gray Brown Brown Gray
Row 19: Brown Gray Gray Gray Brown Gray Gray Gray Brown Brown Gray
Row 20: Brown Gray Brown Brown Brown Gray Brown Brown Gray Gray Gray
Row 21: Gray Gray Brown Gray Gray Gray Brown Brown Gray Brown Brown
Row 22: Brown Brown Brown Gray Brown Brown Gray Gray Gray Brown Brown
Row 23: Brown Gray Gray Gray Brown Brown Gray Brown Brown Brown Gray
Row 24: Brown Gray Brown Brown Gray Gray Gray Brown Brown Brown Gray
Row 25: Gray Gray Brown Brown Gray Brown Brown Brown Brown Brown Red
Row 26: Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Gray
Row 27: Brown Brown Brown Brown Gray Brown Brown Brown Gray Gray Gray
Example 2
Input:
Row 1: Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black Red Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Red Black Black Black Black Black Black Red Black
Row 20: Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Red Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 24: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Red Black
Output:
Row 1: Black Black Black Black Red Black Black Black Black Gray Black Black Black Black Gray Gray Gray Black Black Black
Row 2: Black Black Black Black Gray Black Black Gray Gray Gray Black Black Black Black Gray Black Black Black Gray Gray
Row 3: Black Black Gray Gray Gray Black Black Gray Black Black Black Black Gray Gray Gray Black Black Black Gray Black
Row 4: Black Black Gray Black Black Gray Gray Gray Black Black Black Black Gray Black Black Black Gray Gray Gray Gray
Row 5: Gray Gray Gray Black Black Gray Black Black Black Black Gray Gray Gray Black Black Black Gray Black Black Gray
Row 6: Gray Black Black Gray Gray Gray Black Black Black Black Gray Black Black Black Gray Gray Gray Gray Gray Gray
Row 7: Gray Black Black Gray Black Black Black Black Gray Gray Gray Black Black Black Gray Black Black Gray Black Black
Row 8: Black Gray Gray Gray Black Black Black Black Gray Black Black Black Gray Gray Gray Gray Gray Gray Black Black
Row 9: Black Gray Black Black Black Black Gray Gray Gray Black Black Black Gray Black Black Gray Black Black Black Gray
Row 10: Black Red Black Black Black Black Gray Black Black Black Gray Gray Gray Black Black Red Black Black Black Gray
Row 11: Black Gray Black Black Gray Gray Gray Black Black Black Gray Black Black Black Black Gray Black Gray Gray Gray
Row 12: Gray Gray Black Black Gray Black Black Black Gray Gray Gray Black Black Gray Gray Gray Black Gray Black Black
Row 13: Black Black Gray Gray Gray Black Black Black Gray Black Black Black Black Gray Black Gray Gray Gray Gray Gray
Row 14: Black Black Gray Black Black Black Gray Gray Gray Black Black Gray Gray Gray Black Gray Black Black Gray Black
Row 15: Black Black Red Black Black Black Gray Black Black Black Black Gray Black Gray Gray Gray Gray Gray Gray Black
Row 16: Black Black Gray Black Gray Gray Gray Black Black Gray Gray Gray Black Gray Black Black Gray Black Black Black
Row 17: Gray Gray Gray Black Gray Black Black Black Black Gray Black Gray Gray Gray Gray Gray Gray Black Gray Gray
Row 18: Gray Black Gray Gray Gray Black Black Gray Gray Gray Black Gray Black Black Gray Black Black Black Gray Black
Row 19: Gray Black Gray Black Black Black Black Gray Black Black Black Red Gray Gray Gray Black Black Black Red Black
Row 20: Black Black Red Black Black Gray Gray Gray Black Black Black Gray Gray Black Black Black Black Black Gray Black
Row 21: Black Black Gray Black Black Gray Black Black Black Gray Gray Gray Red Black Black Black Gray Gray Gray Black
Row 22: Gray Gray Gray Gray Gray Gray Black Black Black Gray Black Black Gray Black Black Black Gray Black Gray Gray
Row 23: Gray Black Black Gray Black Black Black Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Black Gray Black
Row 24: Gray Gray Gray Gray Black Black Black Gray Black Black Gray Black Black Black Gray Black Black Black Red Black
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Purple Gray Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Gray Gray Gray Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Purple Gray Purple Purple Purple Purple Purple Gray
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Gray Gray Gray Purple Purple Purple Purple Purple Gray
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Purple Gray Purple Purple Purple Purple Purple Gray Gray Gray
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Gray Gray Gray Purple Purple Purple Purple Purple Gray Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Purple Gray Purple Purple Purple Purple Purple Gray Gray Gray Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Gray Gray Gray Purple Purple Purple Purple Purple Gray Purple Purple Gray Gray
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Purple Gray Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Gray Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Purple Gray Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Gray Gray
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Purple Gray Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Purple Gray Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Gray Gray Gray Purple
Row 15: Purple Purple Purple Purple Purple Purple Gray Gray Gray Purple Gray Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Purple Gray Purple Gray Gray
Row 16: Purple Purple Purple Purple Purple Purple Gray Purple Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Gray Gray Gray Purple Gray Purple
Row 17: Purple Purple Purple Purple Gray Gray Gray Purple Gray Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Purple Gray Purple Purple Purple Yellow Purple
Row 18: Purple Purple Purple Purple Gray Purple Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Gray Gray Gray Purple Purple Purple Gray Purple
Row 19: Purple Purple Purple Purple Yellow Purple Gray Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Purple Gray Purple Purple Purple Gray Gray Gray Purple
Row 20: Purple Purple Purple Purple Gray Purple Yellow Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Purple Yellow Purple Purple Purple Gray Purple Purple Purple
Row 21: Purple Purple Gray Gray Gray Purple Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Purple Purple Purple Gray Purple Gray Gray Gray Purple Purple Purple
Row 22: Purple Purple Gray Purple Gray Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Purple Gray Gray Gray Purple Gray Purple Purple Purple Purple Purple
Row 23: Gray Gray Gray Purple Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Purple Purple Purple Gray Purple Gray Gray Gray Purple Purple Purple Purple Purple
Row 24: Gray Purple Gray Gray Gray Purple Purple Purple Purple Purple Gray Purple Purple Yellow Purple Purple Purple Gray Gray Gray Purple Gray Purple Purple Purple Purple Purple Purple Purple
Row 25: Gray Purple Gray Purple Purple Purple Purple Purple Gray Gray Gray Purple Purple Gray Purple Purple Purple Gray Purple Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 27: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 28: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 29: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 30: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray
Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown
Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown
Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown
Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown
Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Gray Gray Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray
Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown
Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown
Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown
Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown
Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Green Green Purple Green Green Green Green Green Green Green Green Green Purple Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Green Green Green Green Green Green Green Green Green Green Purple Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Green Black Black Black Black Black Black Black Black Green Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Green Black Black Black
Row 12: Black Black Black Black Black Green Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Red Green Green Green Green Green Green Green Green Red Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red Red Green Green Green
Row 5: Green Green Green Green Green Red Green Green Green Green Green Green Green Green Green Green Green Red Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Green Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 4: Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Green Brown Green Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown
Row 7: Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown
Row 8: Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Green
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Green Brown Brown Brown Brown
Row 11: Gray Green Gray Gray Green Green Gray Gray Green Gray Gray Gray Gray Gray Green Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Green Green Gray Gray Gray Gray Gray
Row 13: Gray Gray Green Gray Gray Green Gray Gray Gray Gray Gray Gray Green Green Gray Gray Green
Row 14: Gray Gray Gray Gray Green Green Green Gray Gray Green Green Green Gray Green Gray Gray Green
Row 15: Gray Gray Green Gray Green Gray Gray Gray Gray Gray Green Gray Green Gray Gray Green Gray
Row 16: Gray Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Gray Gray Green
Row 17: Gray Gray Green Green Gray Gray Green Gray Gray Green Green Green Green Gray Green Gray Gray
Row 18: Gray Gray Gray Green Gray Gray Gray Gray Green Gray Gray Gray Green Gray Gray Gray Gray
Row 19: Gray Gray Gray Green Gray Gray Green Green Gray Gray Green Green Gray Gray Green Gray Gray
Row 20: Gray Gray Gray Green Gray Gray Gray Gray Green Gray Green Gray Gray Green Green Green Gray
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Red Green Green Green
Row 4: Green Green Green Green Red Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Red Green Green Green Green Green Green Green Green Green Red Green Green Green Green
Row 7: Green Green Red Green Green Green Green Green Green Green Green Red Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Red Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red Green Green
Row 10: Green Green Green Green Green Green Green Green Red Green Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Blue Blue Pink Pink Blue Pink Pink Pink Pink Pink Blue
Row 3: Blue Pink Pink Blue Pink Blue Pink Blue Pink Pink Pink Pink Pink Pink Blue Pink
Row 4: Blue Blue Pink Blue Blue Pink Pink Blue Pink Blue Pink Pink Pink Pink Pink Blue
Row 5: Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Blue
Row 6: Pink Pink Blue Pink Pink Blue Pink Pink Pink Blue Pink Pink Pink Blue Blue Blue
Row 7: Gray Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Gray
Row 8: Gray Gray Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray Blue
Row 9: Gray Blue Blue Gray Gray Blue Blue Blue Blue Blue Blue Gray Gray Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue
Row 11: Gray Blue Blue Blue Blue Blue Blue Blue Gray Gray Blue Gray Gray Gray Blue Blue
Row 12: Gray Blue Gray Blue Blue Blue Blue Gray Gray Blue Blue Gray Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Red Red Blue Blue Red Blue Blue Blue Blue Blue Red
Row 3: Blue Blue Blue Blue Blue Red Blue Red Blue Blue Blue Blue Blue Blue Red Blue
Row 4: Red Red Blue Red Red Blue Blue Red Blue Red Blue Blue Blue Blue Blue Red
Row 5: Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Red
Row 6: Blue Blue Blue Blue Blue Red Blue Blue Blue Red Blue Blue Blue Red Red Red
Here is the input grid for the test example:
Input:
Row 1: Pink Purple Pink Pink Purple Purple Pink Purple Purple Pink Pink Pink Purple Purple Pink Pink
Row 2: Pink Pink Pink Pink Purple Pink Purple Pink Pink Purple Pink Pink Pink Pink Pink Purple
Row 3: Pink Pink Pink Purple Purple Pink Purple Purple Purple Pink Purple Pink Pink Purple Purple Pink
Row 4: Pink Pink Purple Purple Purple Pink Pink Pink Pink Purple Pink Purple Purple Pink Pink Pink
Row 5: Purple Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Purple Pink
Row 6: Pink Pink Pink Purple Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Purple Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink
Row 8: Pink Purple Purple Purple Purple Pink Purple Pink Pink Purple Pink Pink Pink Purple Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Purple Purple Pink Purple Pink Purple Pink Pink Purple Pink
Row 10: Purple Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Purple Pink Pink Pink
Row 11: Pink Pink Pink Purple Purple Purple Pink Pink Pink Purple Pink Pink Pink Pink Purple Purple
Row 12: Pink Black Pink Pink Pink Black Pink Black Black Pink Pink Black Pink Pink Black Pink
Row 13: Black Pink Pink Pink Pink Black Black Black Pink Black Pink Pink Pink Pink Black Black
Row 14: Pink Black Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Black Pink Pink
Row 15: Black Black Black Pink Pink Black Black Pink Black Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Black Pink Black Black Black Pink Pink Pink Pink Black Pink Pink
Row 17: Pink Pink Pink Pink Pink Black Pink Pink Black Pink Black Black Black Pink Pink Pink
Row 18: Black Black Black Pink Black Pink Pink Black Pink Pink Black Black Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Black Pink Pink Black Pink Pink
Row 20: Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Black
Row 21: Pink Pink Black Pink Pink Pink Pink Black Pink Black Black Pink Black Pink Pink Black
Row 22: Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Pink Red Red Pink Pink Red Pink Pink Red Red Pink Pink Pink Pink Red
Pink Red Red Red Pink Pink Pink Pink Red Pink Red Red Red Red Pink Pink
Red Pink Red Pink Pink Red Pink Pink Pink Red Pink Red Red Pink Pink Red
Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Red Pink Pink Red Red Red
Pink Red Red Red Pink Red Pink Pink Pink Red Red Red Red Pink Pink Red
Red Red Red Pink Red Pink Pink Red Pink Red Pink Pink Pink Red Red Red
Pink Pink Pink Pink Pink Red Red Pink Red Pink Pink Pink Red Red Red Red
Red Pink Pink Pink Pink Red Pink Red Red Pink Pink Red Red Pink Red Red
Red Red Pink Red Red Red Pink Pink Red Pink Red Pink Red Pink Pink Pink
Pink Red Pink Red Red Red Pink Pink Red Pink Pink Red Pink Red Red Pink
Red Pink Red Pink Pink Pink Red Red Red Pink Red Red Red Pink Pink Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Yellow Blue
Row 2: Pink Yellow Yellow
Row 3: Pink Pink Pink
Output:
Row 1: Pink Yellow Blue Pink Yellow Blue
Row 2: Pink Yellow Blue Pink Yellow Yellow
Row 3: Pink Yellow Blue Pink Pink Pink
Row 4: Pink Yellow Blue Blue Blue Blue
Row 5: Pink Yellow Yellow Yellow Yellow Yellow
Row 6: Pink Pink Pink Pink Pink Pink
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black
Row 3: Black Black Orange Orange Orange Orange Orange Orange
Row 4: Black Black Orange Yellow Yellow Yellow Yellow Yellow
Row 5: Black Black Orange Yellow Blue Blue Blue Blue
Row 6: Black Black Orange Yellow Blue Red Red Red
Row 7: Black Black Orange Yellow Blue Red Gray Gray
Row 8: Black Black Orange Yellow Blue Red Gray Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Blue Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Blue Red Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Red Gray Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Blue Red Gray Blue Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Blue Red Gray Blue Orange Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Red Gray Blue Orange Yellow Blue Red Red Red Red Red Red Red Red Red
Row 9: Blue Red Gray Blue Orange Yellow Blue Red Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Blue Red Gray Blue Orange Yellow Blue Red Gray Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Red Gray Blue Orange Yellow Blue Red Gray Blue Orange Orange Orange Orange Orange Orange
Row 12: Blue Red Gray Blue Orange Yellow Blue Red Gray Blue Orange Yellow Yellow Yellow Yellow Yellow
Row 13: Blue Red Gray Blue Orange Yellow Blue Red Gray Blue Orange Yellow Blue Blue Blue Blue
Row 14: Blue Red Gray Blue Orange Yellow Blue Red Gray Blue Orange Yellow Blue Red Red Red
Row 15: Blue Red Gray Blue Orange Yellow Blue Red Gray Blue Orange Yellow Blue Red Gray Gray
Row 16: Blue Red Gray Blue Orange Yellow Blue Red Gray Blue Orange Yellow Blue Red Gray Blue
Example 3
Input:
Row 1: Yellow Blue Blue Orange Orange Red
Row 2: Yellow Blue Blue Orange Orange Orange
Row 3: Yellow Blue Blue Orange Orange Orange
Row 4: Yellow Blue Blue Blue Blue Blue
Row 5: Yellow Blue Blue Blue Blue Blue
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Blue Blue Orange Orange Red Yellow Blue Blue Orange Orange Red
Row 2: Yellow Blue Blue Orange Orange Red Yellow Blue Blue Orange Orange Orange
Row 3: Yellow Blue Blue Orange Orange Red Yellow Blue Blue Orange Orange Orange
Row 4: Yellow Blue Blue Orange Orange Red Yellow Blue Blue Blue Blue Blue
Row 5: Yellow Blue Blue Orange Orange Red Yellow Blue Blue Blue Blue Blue
Row 6: Yellow Blue Blue Orange Orange Red Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Blue Blue Orange Orange Red Red Red Red Red Red Red
Row 8: Yellow Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Yellow Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Here is the input grid for the test example:
Input:
Row 1: Pink Yellow Pink Yellow Gray
Row 2: Yellow Yellow Pink Yellow Gray
Row 3: Pink Pink Pink Yellow Gray
Row 4: Yellow Yellow Yellow Yellow Gray
Row 5: Gray Gray Gray Gray Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Yellow Pink Yellow Gray Pink Yellow Pink Yellow Gray
Yellow Yellow Pink Yellow Gray Pink Yellow Pink Yellow Gray
Pink Pink Pink Yellow Gray Pink Yellow Pink Yellow Gray
Yellow Yellow Yellow Yellow Gray Pink Yellow Pink Yellow Gray
Gray Gray Gray Gray Gray Pink Yellow Pink Yellow Gray
Pink Pink Pink Pink Pink Pink Yellow Pink Yellow Gray
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Gray
Pink Pink Pink Pink Pink Pink Pink Pink Yellow Gray
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray
Row 2: Gray Gray Brown Brown Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Gray Gray
Row 3: Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Green Green Green Green Green Green Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Green Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Green Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Brown Brown Brown Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Green Green Green Green Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Green Gray Green Gray Gray Gray Gray Gray Gray Gray Green Green
Row 9: Gray Gray Black Black Black Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Green
Row 10: Gray Gray Black Gray Black Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Gray Gray Gray Gray Gray Green
Row 11: Gray Gray Black Gray Black Gray Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Green Green
Row 12: Gray Gray Gray Gray Black Gray Brown Gray Green Green Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray
Row 13: Brown Brown Brown Gray Gray Gray Brown Gray Gray Green Gray Gray Gray Purple Gray Gray Gray Gray Black Gray Gray Gray
Row 14: Brown Gray Gray Gray Gray Gray Brown Gray Green Green Gray Gray Purple Purple Gray Gray Gray Black Black Gray Gray Gray
Row 15: Brown Brown Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray
Row 2: Gray Gray Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Blue Gray Gray
Row 3: Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Pink Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Red Red Red Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Blue Gray Blue Gray Gray Gray Gray Gray Gray Gray Pink Pink
Row 9: Gray Gray Red Red Red Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Pink
Row 10: Gray Gray Red Gray Red Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Gray Gray Gray Gray Gray Pink
Row 11: Gray Gray Red Gray Red Gray Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Pink Pink
Row 12: Gray Gray Gray Gray Red Gray Blue Gray Pink Pink Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray
Row 13: Pink Pink Pink Gray Gray Gray Blue Gray Gray Pink Gray Gray Gray Blue Gray Gray Gray Gray Blue Gray Gray Gray
Row 14: Pink Gray Gray Gray Gray Gray Blue Gray Pink Pink Gray Gray Blue Blue Gray Gray Gray Blue Blue Gray Gray Gray
Row 15: Pink Pink Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Example 2
Input:
Row 1: Purple Purple Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 3: Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 4: Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Gray Purple Gray Purple Purple Purple Yellow Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Purple Yellow Purple Purple Purple Purple
Row 9: Gray Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple
Row 10: Gray Gray Gray Gray Gray Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Pink Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Blue
Row 3: Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Blue Purple Blue Purple Purple Purple Blue Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Blue Purple Blue Purple Purple Purple Purple
Row 9: Pink Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple
Row 10: Pink Pink Pink Pink Pink Purple Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Gray Gray Gray Purple Purple Purple Gray Gray Gray Gray Brown Brown Brown Brown Gray Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Brown Gray Gray Brown Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Brown Gray Gray Brown Gray Gray Gray Gray Gray Yellow Gray Gray Gray Purple Gray Gray Purple Gray
Row 4: Gray Gray Purple Purple Purple Gray Gray Gray Gray Gray Brown Gray Gray Brown Gray Gray Gray Gray Gray Yellow Gray Gray Gray Purple Purple Purple Purple Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Brown Brown Brown Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Gray Purple Gray Purple Gray Green Gray Gray
Row 7: Gray Brown Gray Gray Gray Gray Gray Brown Gray Gray Brown Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Gray Green Gray Gray
Row 8: Gray Brown Gray Gray Gray Gray Gray Brown Gray Gray Brown Brown Brown Brown Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Green Gray Gray
Row 9: Gray Brown Gray Brown Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray
Row 10: Gray Brown Gray Brown Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Green Green Gray Gray
Row 11: Gray Brown Brown Brown Gray Brown Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Green Green Green Green Green Gray Gray Gray Gray
Row 12: Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Yellow Yellow Yellow Gray Gray Gray Green Gray Gray Gray Gray Purple Gray
Row 13: Brown Gray Gray Gray Gray Purple Purple Gray Gray Purple Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Gray Gray Purple Purple Gray
Row 14: Brown Gray Brown Gray Gray Gray Purple Gray Purple Purple Gray Purple Gray Purple Gray Green Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Brown Brown Brown Gray Gray Gray Purple Gray Gray Gray Gray Purple Gray Purple Gray Gray Green Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray
Row 16: Gray Gray Brown Gray Purple Purple Purple Gray Gray Gray Gray Purple Gray Purple Gray Gray Green Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Purple Gray Purple Gray Purple Purple Purple Gray Purple Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Gray Gray Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Brown Brown Brown Gray Gray Gray Gray Gray Purple Gray Gray Brown Gray Gray Brown Gray Gray
Row 21: Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown Gray Gray
Row 22: Gray Green Green Green Green Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Red Red Red Gray Gray Gray Gray Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Pink Gray Gray Pink Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Pink Gray Gray Pink Gray Gray Gray Gray Gray Pink Gray Gray Gray Pink Gray Gray Pink Gray
Row 4: Gray Gray Red Red Red Gray Gray Gray Gray Gray Pink Gray Gray Pink Gray Gray Gray Gray Gray Pink Gray Gray Gray Pink Pink Pink Pink Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Red Red Red Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Gray Red Gray Red Gray Blue Gray Gray
Row 7: Gray Red Gray Gray Gray Gray Gray Red Gray Gray Pink Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Red Red Red Gray Blue Gray Gray
Row 8: Gray Red Gray Gray Gray Gray Gray Red Gray Gray Pink Pink Pink Pink Gray Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Blue Gray Gray
Row 9: Gray Red Gray Red Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray
Row 10: Gray Red Gray Red Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Blue Blue Gray Gray
Row 11: Gray Red Red Red Gray Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Red Red Red Red Red Gray Gray Gray Gray
Row 12: Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Blue Blue Blue Gray Gray Gray Red Gray Gray Gray Gray Blue Gray
Row 13: Red Gray Gray Gray Gray Pink Pink Gray Gray Blue Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Gray Gray Blue Blue Gray
Row 14: Red Gray Red Gray Gray Gray Pink Gray Blue Blue Gray Pink Gray Pink Gray Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Red Red Red Gray Gray Gray Pink Gray Gray Gray Gray Pink Gray Pink Gray Gray Blue Gray Gray Red Red Red Red Red Red Gray Gray Gray
Row 16: Gray Gray Red Gray Pink Pink Pink Gray Gray Gray Gray Pink Gray Pink Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Red Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Pink Gray Pink Gray Pink Pink Pink Gray Red Gray Gray Gray Gray Red Red Red Red Red Red Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Blue Blue Blue Gray Gray Gray Gray Gray Red Gray Gray Pink Gray Gray Pink Gray Gray
Row 21: Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Gray Gray
Row 22: Gray Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Black Black Black Purple Purple Purple
Row 2: Purple Purple Purple Orange Purple Purple Purple Purple Purple Gray Purple Purple Purple Black Purple Purple Purple
Row 3: Purple Purple Orange Orange Orange Purple Purple Purple Purple Gray Purple Purple Purple Black Purple Purple Purple
Row 4: Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Black Black Purple Purple Purple
Row 5: Gray Purple Purple Purple Purple Purple Gray Purple Purple Gray Purple Brown Purple Purple Purple Purple Purple
Row 6: Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple
Row 7: Gray Purple Gray Purple Purple Brown Brown Brown Brown Purple Purple Brown Purple Purple Purple Purple Brown
Row 8: Gray Gray Gray Purple Purple Brown Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown
Row 9: Purple Purple Gray Purple Purple Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown
Row 10: Purple Purple Gray Purple Purple Purple Purple Purple Purple Black Black Black Purple Purple Purple Purple Brown
Row 11: Purple Purple Gray Purple Yellow Purple Purple Purple Purple Purple Purple Black Purple Orange Purple Purple Brown
Row 12: Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Black Purple Orange Purple Purple Brown
Row 13: Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Orange Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Orange Purple Purple Purple
Row 15: Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Orange Orange Purple Purple
Row 16: Purple Purple Yellow Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Purple Purple Purple
Row 17: Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Red Red Purple Purple Purple Purple Purple Purple Pink Pink Pink Purple Purple Purple
Purple Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Pink Purple Purple Purple
Purple Purple Red Red Red Purple Purple Purple Purple Red Purple Purple Purple Pink Purple Purple Purple
Red Purple Purple Purple Purple Purple Red Red Red Red Purple Purple Pink Pink Purple Purple Purple
Red Purple Purple Purple Purple Purple Red Purple Purple Red Purple Red Purple Purple Purple Purple Purple
Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple
Red Purple Red Purple Purple Pink Pink Pink Pink Purple Purple Red Purple Purple Purple Purple Red
Red Red Red Purple Purple Pink Purple Purple Purple Purple Purple Red Red Red Red Red Red
Purple Purple Red Purple Purple Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Red
Purple Purple Red Purple Purple Purple Purple Purple Purple Blue Blue Blue Purple Purple Purple Purple Red
Purple Purple Red Purple Blue Purple Purple Purple Purple Purple Purple Blue Purple Blue Purple Purple Red
Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Blue Purple Blue Purple Purple Red
Purple Purple Purple Purple Blue Blue Blue Blue Blue Purple Purple Purple Purple Blue Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Blue Purple Purple Purple
Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Blue Blue Purple Purple
Purple Purple Blue Purple Purple Purple Purple Purple Blue Blue Blue Blue Purple Purple Purple Purple Purple
Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Blue
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Gray Gray Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Gray Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Brown
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Brown
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Brown
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Yellow
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Yellow
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Yellow
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Purple Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 24: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 25: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 26: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 27: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 28: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 29: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Red Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 24: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 25: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 26: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 27: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 28: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 29: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Brown Brown Brown Brown Green Brown Brown Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Brown Brown Brown Brown Blue Brown Brown Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow Yellow Yellow Red Black Black Black Red Yellow Yellow Red Red Purple Red Purple
Row 2: Yellow Yellow Red Red Red Black Black Black Red Yellow Red Red Red Red Purple Purple
Row 3: Yellow Red Yellow Yellow Red Black Black Black Red Yellow Yellow Yellow Red Purple Purple Red
Row 4: Red Red Yellow Yellow Red Black Red Black Red Red Yellow Yellow Red Red Red Red
Row 5: Yellow Red Red Red Red Black Black Black Red Red Yellow Red Red Red Purple Purple
Row 6: Yellow Yellow Yellow Red Red Black Black Black Red Red Yellow Yellow Red Purple Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Black Black Red Black Red Blue Red Red Red Red Green Green Red Black Black Black
Row 9: Black Black Black Red Red Blue Blue Red Red Red Green Green Red Black Black Red
Row 10: Red Black Red Black Red Red Blue Blue Red Red Green Green Red Black Black Black
Row 11: Black Red Black Black Red Blue Red Blue Red Green Green Green Red Black Black Red
Row 12: Black Black Black Black Red Blue Blue Red Red Green Red Green Red Black Black Red
Row 13: Black Red Black Black Red Blue Blue Blue Red Green Red Green Red Black Red Red
Row 14: Black Black Red Black Red Red Blue Blue Red Red Red Red Red Black Black Black
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Brown Brown Brown Red Red Green Green Red Red Blue Blue Blue Red Blue Blue Blue
Row 17: Brown Red Brown Brown Red Green Green Green Red Blue Blue Blue Red Blue Blue Red
Row 18: Brown Brown Red Brown Red Green Green Green Red Blue Blue Blue Red Red Blue Blue
Row 19: Brown Brown Red Brown Red Red Red Green Red Blue Blue Blue Red Blue Red Blue
Row 20: Red Red Brown Brown Red Green Green Green Red Blue Blue Red Red Blue Red Red
Row 21: Brown Brown Red Brown Red Green Green Red Red Blue Blue Blue Red Blue Red Red
Row 22: Brown Brown Brown Brown Red Red Green Red Red Blue Blue Blue Red Blue Blue Blue
Row 23: Brown Brown Brown Red Red Red Green Green Red Blue Red Blue Red Red Blue Blue
Row 24: Brown Brown Brown Brown Red Green Green Green Red Blue Blue Blue Red Red Blue Red
Row 25: Brown Red Red Brown Red Green Red Green Red Blue Blue Blue Red Red Blue Blue
Row 26: Brown Brown Brown Red Red Green Green Green Red Blue Blue Blue Red Red Red Blue
Row 27: Brown Brown Brown Brown Red Green Green Green Red Blue Red Blue Red Blue Red Red
Row 28: Red Brown Brown Brown Red Green Green Green Red Blue Blue Blue Red Red Blue Blue
Row 29: Brown Brown Brown Brown Red Red Green Green Red Blue Blue Blue Red Blue Red Red
Row 30: Brown Red Red Brown Red Red Green Red Red Blue Blue Blue Red Red Red Red
Output:
Row 1: Yellow Black Yellow Purple
Row 2: Black Blue Green Black
Row 3: Brown Green Blue Blue
Example 2
Input:
Row 1: Orange Orange Brown Orange Brown Brown Purple Purple Purple Brown Purple Brown Orange Brown Brown Orange Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Brown Brown Brown Brown Orange Brown Purple Purple Purple Purple Purple Brown Orange Brown Orange Orange Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Brown Brown Brown Orange Orange Brown Purple Purple Purple Purple Brown Brown Orange Brown Orange Orange Brown Brown Yellow Yellow Yellow Yellow Yellow
Row 4: Brown Orange Orange Brown Orange Brown Purple Purple Purple Brown Brown Brown Orange Brown Orange Orange Brown Yellow Yellow Brown Yellow Yellow Yellow
Row 5: Orange Orange Orange Orange Brown Brown Purple Brown Purple Purple Brown Brown Orange Orange Brown Orange Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Orange Orange Brown Brown Brown Brown Brown Purple Purple Purple Purple Brown Brown Orange Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Black Black Black Brown Brown Brown Black Black Black Brown Black Brown Purple Brown Brown Brown Brown Gray Gray Gray Gray Brown Gray
Row 9: Brown Brown Brown Black Brown Brown Black Brown Brown Brown Brown Brown Purple Purple Purple Purple Brown Gray Brown Gray Brown Gray Gray
Row 10: Black Black Brown Black Black Brown Black Brown Black Black Black Brown Purple Brown Purple Purple Brown Gray Gray Gray Gray Gray Brown
Row 11: Black Black Black Brown Black Brown Black Brown Black Brown Black Brown Brown Purple Purple Purple Brown Gray Gray Gray Brown Gray Gray
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Gray Brown Gray Gray Gray Brown Orange Orange Orange Orange Orange Brown Brown Yellow Yellow Brown Brown Brown Black Black Brown Black Black
Row 14: Gray Brown Brown Gray Gray Brown Brown Orange Orange Brown Orange Brown Yellow Yellow Brown Brown Brown Black Black Black Brown Brown Black
Row 15: Gray Gray Gray Gray Brown Brown Brown Orange Brown Brown Orange Brown Yellow Yellow Brown Yellow Brown Black Black Brown Black Black Black
Output:
Row 1: Orange Purple Orange Yellow
Row 2: Black Black Purple Gray
Row 3: Gray Orange Yellow Black
Example 3
Input:
Row 1: Orange Orange Orange Orange Green Green Orange Green Green Green Green Green
Row 2: Green Orange Green Green Orange Orange Orange Green Blue Blue Blue Green
Row 3: Orange Green Orange Orange Green Green Green Green Blue Blue Blue Blue
Row 4: Orange Orange Orange Orange Orange Green Green Green Green Blue Green Green
Row 5: Orange Orange Orange Orange Orange Orange Orange Green Green Blue Green Green
Row 6: Green Orange Orange Orange Orange Orange Orange Green Green Blue Blue Green
Row 7: Green Orange Green Orange Orange Orange Orange Green Blue Blue Blue Blue
Row 8: Green Green Orange Orange Orange Green Green Green Blue Blue Blue Blue
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Gray Green Green Gray Gray Green Green Blue Blue Blue Blue
Row 11: Green Gray Gray Gray Gray Gray Gray Green Blue Green Green Green
Row 12: Gray Green Green Gray Green Green Gray Green Green Blue Blue Blue
Row 13: Green Gray Green Gray Green Gray Gray Green Green Blue Blue Green
Row 14: Gray Green Gray Gray Green Gray Gray Green Green Blue Blue Blue
Row 15: Green Gray Gray Green Gray Green Green Green Green Green Green Green
Row 16: Gray Gray Gray Gray Gray Gray Gray Green Blue Green Blue Blue
Row 17: Gray Gray Gray Gray Gray Green Gray Green Green Blue Green Blue
Row 18: Gray Gray Gray Gray Green Gray Green Green Green Blue Blue Blue
Row 19: Green Gray Gray Green Gray Gray Green Green Blue Blue Blue Blue
Row 20: Gray Gray Gray Gray Gray Gray Green Green Blue Blue Blue Blue
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Pink Pink Pink Green Green Pink Green Green Pink Green Pink Pink
Row 23: Pink Green Pink Green Green Pink Green Green Green Green Pink Green
Row 24: Pink Green Green Pink Pink Green Pink Green Pink Pink Green Green
Row 25: Green Pink Pink Green Green Green Pink Green Green Green Green Green
Row 26: Green Pink Pink Green Pink Green Pink Green Green Green Pink Green
Row 27: Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink
Row 28: Pink Pink Pink Pink Pink Pink Pink Green Pink Green Green Pink
Row 29: Green Pink Pink Pink Green Pink Green Green Green Pink Pink Pink
Row 30: Pink Pink Green Pink Green Green Pink Green Pink Pink Pink Pink
Output:
Row 1: Orange Blue
Row 2: Gray Blue
Row 3: Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Brown Green Brown Brown Brown Green Green Pink Pink Green Green Green Red Green Red Green Green Orange Orange Green Green Yellow Yellow Green
Row 2: Brown Brown Brown Brown Green Brown Green Green Pink Green Green Red Red Green Green Green Orange Green Orange Green Yellow Yellow Yellow Yellow
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Red Green Green Red Red Red Green Brown Brown Green Green Pink Pink Green Pink Green Green Brown Brown Green Pink Pink Pink Pink
Row 5: Green Red Red Green Red Red Green Brown Brown Brown Green Green Green Pink Pink Green Brown Green Green Green Green Pink Pink Green
Row 6: Green Green Red Green Red Red Green Brown Green Brown Green Pink Green Pink Pink Green Brown Brown Brown Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Green Orange Green Orange Green Yellow Yellow Yellow Yellow Green Brown Brown Brown Green Red Red Green Red
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Green Orange Orange Orange Green Yellow Yellow Yellow Yellow Green Green Brown Brown Green Green Red Red Red
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Green Green Orange Orange Green Green Green Green Yellow Green Green Green Brown Green Red Red Red Red
Row 11: Green Yellow Yellow Yellow Yellow Yellow Green Green Orange Orange Green Yellow Yellow Green Green Green Brown Brown Brown Green Red Red Red Red
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Gray Gray Green Gray Gray Gray Green Yellow Green Yellow Green Red Green Green Red Green Pink Green Pink Green Red Red Green Red
Row 14: Gray Gray Gray Gray Gray Gray Green Yellow Green Yellow Green Red Red Red Green Green Green Pink Green Green Red Red Red Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Pink Red Orange Yellow
Red Brown Pink Brown Pink
Yellow Orange Yellow Brown Red
Gray Yellow Red Pink Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 3
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray
Row 24: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray
Row 24: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Blue Yellow Brown
Row 2: Brown Brown Brown Purple
Output:
Row 1: Brown Yellow Brown Brown
Row 2: Brown Brown Brown Brown
Row 3: Brown Brown Brown Purple
Row 4: Brown Brown Brown Brown
Example 2
Input:
Row 1: Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow
Row 4: Yellow Yellow Brown
Row 5: Yellow Green Blue
Row 6: Yellow Green Yellow
Row 7: Yellow Blue Blue
Row 8: Green Green Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Blue
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Blue
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Green Yellow Yellow Green Yellow Yellow Yellow
Example 3
Input:
Row 1: Blue Blue Blue Green Black Green
Row 2: Blue Red Red Gray Pink Pink
Row 3: Blue Red Red Brown Brown Gray
Row 4: Blue Blue Blue Yellow Red Brown
Row 5: Blue Red Red Yellow Orange Black
Output:
Row 1: Green Green Green Black Black Black Green Green Green
Row 2: Green Red Red Black Red Red Green Red Red
Row 3: Green Red Red Black Red Red Green Red Red
Row 4: Green Green Green Black Black Black Green Green Green
Row 5: Green Red Red Black Red Red Green Red Red
Row 6: Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 7: Gray Red Red Pink Red Red Pink Red Red
Row 8: Gray Red Red Pink Red Red Pink Red Red
Row 9: Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 10: Gray Red Red Pink Red Red Pink Red Red
Row 11: Brown Brown Brown Brown Brown Brown Gray Gray Gray
Row 12: Brown Red Red Brown Red Red Gray Red Red
Row 13: Brown Red Red Brown Red Red Gray Red Red
Row 14: Brown Brown Brown Brown Brown Brown Gray Gray Gray
Row 15: Brown Red Red Brown Red Red Gray Red Red
Row 16: Yellow Yellow Yellow Red Red Red Brown Brown Brown
Row 17: Yellow Red Red Red Red Red Brown Red Red
Row 18: Yellow Red Red Red Red Red Brown Red Red
Row 19: Yellow Yellow Yellow Red Red Red Brown Brown Brown
Row 20: Yellow Red Red Red Red Red Brown Red Red
Row 21: Yellow Yellow Yellow Orange Orange Orange Black Black Black
Row 22: Yellow Red Red Orange Red Red Black Red Red
Row 23: Yellow Red Red Orange Red Red Black Red Red
Row 24: Yellow Yellow Yellow Orange Orange Orange Black Black Black
Row 25: Yellow Red Red Orange Red Red Black Red Red
Here is the input grid for the test example:
Input:
Row 1: Gray Brown Gray Brown Brown Gray Gray Gray Orange Yellow
Row 2: Gray Brown Gray Brown Brown Purple Gray Gray Black Pink
Row 3: Brown Gray Brown Brown Brown Gray Gray Yellow Gray Black
Row 4: Brown Brown Brown Brown Brown Purple Gray Gray Gray Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Orange Orange Gray Yellow Gray Yellow Yellow
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Orange Orange Gray Yellow Gray Yellow Yellow
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Orange Orange Orange Yellow Gray Yellow Yellow Yellow
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow
Gray Purple Gray Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Black Black Gray Pink Gray Pink Pink
Gray Purple Gray Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Black Black Gray Pink Gray Pink Pink
Purple Gray Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Black Black Black Pink Gray Pink Pink Pink
Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Black Black Pink Pink Pink Pink Pink
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Yellow Yellow Gray Gray Gray Gray Gray Gray Black Gray Black Black
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Yellow Yellow Gray Gray Gray Gray Gray Gray Black Gray Black Black
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray Black Gray Black Black Black
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Black Black Black Black Black
Gray Purple Gray Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Green Green
Gray Purple Gray Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Green Green
Purple Gray Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Green Green Green
Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Blue Orange Orange Orange Orange Blue Blue Orange Orange Blue Orange Orange Orange Orange Blue Blue Orange Orange Blue Orange Orange Orange Orange Blue Blue
Row 2: Orange Orange Blue Orange Orange Orange Orange Orange Blue Orange Orange Blue Orange Orange Orange Orange Orange Blue Orange Orange Blue Orange Orange Orange Orange Orange
Row 3: Orange Blue Orange Blue Orange Blue Orange Orange Blue Orange Blue Orange Blue Orange Blue Orange Orange Blue Orange Blue Orange Blue Orange Blue Orange Orange
Row 4: Blue Orange Orange Blue Orange Blue Orange Blue Blue Blue Orange Orange Blue Orange Blue Orange Blue Blue Blue Orange Orange Blue Orange Blue Orange Blue
Row 5: Orange Black Black Black Black Black Black Black Black Black Black Black Black Blue Blue Blue Orange Blue Orange Blue Orange Orange Blue Blue Blue Orange
Row 6: Blue Black Black Black Black Black Black Black Black Black Black Black Black Blue Blue Blue Blue Blue Blue Orange Blue Orange Blue Blue Blue Blue
Row 7: Blue Black Black Black Black Black Black Black Black Black Black Black Black Orange Blue Blue Orange Blue Blue Blue Orange Blue Orange Blue Blue Orange
Row 8: Orange Black Black Black Black Black Black Black Black Black Black Black Black Blue Orange Orange Blue Blue Orange Blue Orange Orange Blue Orange Orange Blue
Row 9: Orange Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Blue Blue Orange Orange Blue Orange Orange Orange Orange Blue Blue
Row 10: Orange Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Blue Orange Orange Blue Orange Orange Orange Orange Orange
Row 11: Orange Black Black Black Black Black Black Black Black Black Black Black Black Orange Blue Orange Orange Blue Orange Blue Orange Blue Orange Blue Orange Orange
Row 12: Blue Black Black Black Black Black Black Black Black Black Black Black Black Orange Blue Orange Blue Blue Blue Orange Orange Blue Orange Blue Orange Blue
Row 13: Orange Blue Orange Orange Blue Blue Blue Orange Blue Orange Blue Orange Orange Blue Blue Blue Orange Blue Orange Blue Orange Orange Blue Blue Blue Orange
Row 14: Blue Orange Blue Orange Blue Blue Blue Blue Blue Blue Orange Blue Orange Blue Blue Blue Blue Blue Blue Orange Blue Orange Blue Blue Blue Blue
Row 15: Blue Blue Orange Blue Orange Blue Blue Orange Blue Blue Blue Orange Blue Orange Blue Blue Orange Blue Blue Blue Orange Blue Orange Blue Blue Orange
Row 16: Orange Blue Orange Orange Blue Orange Orange Blue Blue Orange Blue Orange Orange Blue Orange Orange Blue Blue Orange Blue Orange Orange Blue Orange Orange Blue
Row 17: Orange Blue Orange Orange Orange Orange Blue Blue Orange Orange Blue Orange Orange Orange Orange Blue Blue Orange Orange Blue Orange Orange Orange Orange Blue Blue
Row 18: Orange Orange Blue Orange Orange Orange Orange Orange Blue Orange Orange Blue Orange Orange Orange Orange Orange Blue Orange Orange Blue Orange Orange Orange Orange Orange
Row 19: Orange Blue Orange Blue Orange Blue Orange Orange Blue Orange Blue Orange Blue Orange Blue Orange Orange Blue Orange Blue Orange Blue Orange Blue Orange Orange
Output:
Row 1: Blue Orange Orange Blue Blue Blue Orange Blue Orange Blue Orange Orange
Row 2: Orange Blue Orange Blue Blue Blue Blue Blue Blue Orange Blue Orange
Row 3: Blue Orange Blue Orange Blue Blue Orange Blue Blue Blue Orange Blue
Row 4: Blue Orange Orange Blue Orange Orange Blue Blue Orange Blue Orange Orange
Row 5: Blue Orange Orange Orange Orange Blue Blue Orange Orange Blue Orange Orange
Row 6: Orange Blue Orange Orange Orange Orange Orange Blue Orange Orange Blue Orange
Row 7: Blue Orange Blue Orange Blue Orange Orange Blue Orange Blue Orange Blue
Row 8: Orange Orange Blue Orange Blue Orange Blue Blue Blue Orange Orange Blue
Example 2
Input:
Row 1: Pink Pink Yellow Green Pink Pink Pink Yellow Green Pink Pink Pink Yellow Green Pink Pink Pink Yellow Green Pink Pink Pink Yellow Green Pink Pink Pink Yellow
Row 2: Yellow Yellow Gray Brown Red Yellow Yellow Gray Brown Red Yellow Yellow Gray Brown Red Yellow Yellow Gray Brown Red Yellow Yellow Gray Brown Red Yellow Yellow Gray
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Blue Gray Orange Orange Orange
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Yellow Green Pink Pink Pink Yellow
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Brown Red Yellow Yellow Gray
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Blue Gray Orange Orange Orange
Row 7: Pink Pink Yellow Green Pink Pink Pink Yellow Green Pink Pink Pink Yellow Green Pink Pink Pink Yellow Green Pink Pink Pink Yellow Green Pink Pink Pink Yellow
Row 8: Yellow Yellow Gray Brown Red Yellow Yellow Gray Brown Red Yellow Yellow Gray Brown Red Yellow Yellow Gray Brown Red Yellow Yellow Gray Brown Red Yellow Yellow Gray
Row 9: Orange Orange Orange Blue Gray Orange Orange Orange Blue Gray Orange Orange Orange Blue Gray Orange Orange Orange Blue Gray Orange Orange Orange Blue Gray Orange Orange Orange
Row 10: Pink Pink Yellow Green Pink Pink Pink Yellow Green Pink Pink Pink Yellow Green Pink Pink Pink Yellow Green Pink Pink Pink Yellow Green Pink Pink Pink Yellow
Row 11: Yellow Yellow Gray Brown Red Yellow Yellow Gray Brown Red Yellow Yellow Gray Brown Red Yellow Yellow Gray Brown Red Yellow Yellow Gray Brown Red Yellow Yellow Gray
Row 12: Orange Orange Orange Blue Gray Orange Orange Orange Blue Gray Orange Orange Orange Blue Gray Orange Orange Orange Blue Gray Orange Orange Orange Blue Gray Orange Orange Orange
Output:
Row 1: Orange Orange Orange Blue Gray Orange Orange Orange Blue Gray Orange Orange Orange Blue Gray Orange Orange Orange Blue Gray Orange Orange
Row 2: Pink Pink Yellow Green Pink Pink Pink Yellow Green Pink Pink Pink Yellow Green Pink Pink Pink Yellow Green Pink Pink Pink
Row 3: Yellow Yellow Gray Brown Red Yellow Yellow Gray Brown Red Yellow Yellow Gray Brown Red Yellow Yellow Gray Brown Red Yellow Yellow
Row 4: Orange Orange Orange Blue Gray Orange Orange Orange Blue Gray Orange Orange Orange Blue Gray Orange Orange Orange Blue Gray Orange Orange
Example 3
Input:
Row 1: Red Pink Red Red Pink Red Red Pink Red Red Pink Red
Row 2: Green Red Orange Green Red Orange Green Red Orange Green Red Orange
Row 3: Pink Orange Green Pink Orange Green Pink Orange Green Pink Orange Green
Row 4: Green Green Pink Green Green Pink Green Green Pink Green Green Pink
Row 5: Red Green Red Red Green Red Red Green Red Red Green Red
Row 6: Pink Green Black Black Black Black Black Green Red Pink Green Red
Row 7: Red Pink Black Black Black Black Black Pink Red Red Pink Red
Row 8: Green Red Black Black Black Black Black Red Orange Green Red Orange
Row 9: Pink Orange Black Black Black Black Black Orange Green Pink Orange Green
Row 10: Green Green Black Black Black Black Black Green Pink Green Green Pink
Row 11: Red Green Black Black Black Black Black Green Red Red Green Red
Row 12: Pink Green Black Black Black Black Black Green Red Pink Green Red
Row 13: Red Pink Black Black Black Black Black Pink Red Red Pink Red
Row 14: Green Red Black Black Black Black Black Red Orange Green Red Orange
Row 15: Pink Orange Black Black Black Black Black Orange Green Pink Orange Green
Row 16: Green Green Black Black Black Black Black Green Pink Green Green Pink
Row 17: Red Green Black Black Black Black Black Green Red Red Green Red
Row 18: Pink Green Red Pink Green Red Pink Green Red Pink Green Red
Row 19: Red Pink Red Red Pink Red Red Pink Red Red Pink Red
Row 20: Green Red Orange Green Red Orange Green Red Orange Green Red Orange
Output:
Row 1: Red Pink Green Red Pink
Row 2: Red Red Pink Red Red
Row 3: Orange Green Red Orange Green
Row 4: Green Pink Orange Green Pink
Row 5: Pink Green Green Pink Green
Row 6: Red Red Green Red Red
Row 7: Red Pink Green Red Pink
Row 8: Red Red Pink Red Red
Row 9: Orange Green Red Orange Green
Row 10: Green Pink Orange Green Pink
Row 11: Pink Green Green Pink Green
Row 12: Red Red Green Red Red
Here is the input grid for the test example:
Input:
Row 1: Red Pink Orange Orange Orange Purple Brown Red Pink Orange Orange Orange Purple Brown Red Pink Orange Orange Orange Purple Brown Red Pink Orange
Row 2: Orange Brown Green Orange Gray Red Purple Orange Brown Green Orange Gray Red Purple Orange Brown Green Orange Gray Red Purple Orange Brown Green
Row 3: Green Gray Green Brown Pink Gray Pink Green Gray Green Brown Pink Gray Pink Green Gray Green Brown Pink Gray Pink Green Gray Green
Row 4: Pink Red Green Green Pink Pink Gray Pink Red Green Green Pink Pink Gray Pink Red Green Green Pink Pink Gray Pink Red Green
Row 5: Orange Orange Orange Blue Green Green Purple Orange Orange Orange Blue Green Green Purple Orange Orange Orange Blue Green Green Purple Orange Orange Orange
Row 6: Orange Gray Gray Gray Pink Green Pink Orange Gray Gray Gray Pink Green Pink Orange Gray Gray Gray Pink Green Pink Orange Gray Gray
Row 7: Brown Pink Gray Gray Green Gray Gray Brown Pink Gray Gray Green Gray Gray Brown Pink Gray Gray Green Gray Gray Brown Pink Gray
Row 8: Black Black Black Black Black Orange Pink Green Red Red Brown Pink Orange Pink Green Red Red Brown Pink Orange Pink Green Red Red
Row 9: Gray Gray Brown Purple Red Blue Purple Gray Gray Brown Purple Red Blue Purple Gray Gray Brown Purple Red Blue Purple Gray Gray Brown
Row 10: Red Pink Orange Orange Orange Purple Brown Red Pink Orange Orange Orange Purple Brown Red Pink Orange Orange Orange Purple Brown Red Pink Orange
Row 11: Orange Brown Green Orange Gray Red Purple Orange Brown Green Orange Gray Red Purple Orange Brown Green Orange Gray Red Purple Orange Brown Green
Row 12: Green Gray Green Brown Pink Gray Pink Green Gray Green Brown Pink Gray Pink Green Gray Green Brown Pink Gray Pink Green Gray Green
Row 13: Pink Red Green Green Pink Pink Gray Pink Red Green Green Pink Pink Gray Pink Red Green Green Pink Pink Gray Pink Red Green
Row 14: Orange Orange Orange Blue Green Green Purple Orange Orange Orange Blue Green Green Purple Orange Orange Orange Blue Green Green Purple Orange Orange Orange
Row 15: Orange Gray Gray Gray Pink Green Pink Orange Gray Gray Gray Pink Green Pink Orange Gray Gray Gray Pink Green Pink Orange Gray Gray
Row 16: Brown Pink Gray Gray Green Gray Gray Brown Pink Gray Gray Green Gray Gray Brown Pink Gray Gray Green Gray Gray Brown Pink Gray
Row 17: Green Red Red Brown Pink Orange Pink Green Red Red Brown Pink Orange Pink Green Red Red Brown Pink Orange Pink Green Red Red
Row 18: Gray Gray Brown Purple Red Blue Purple Gray Gray Brown Purple Red Blue Purple Gray Gray Brown Purple Red Blue Purple Gray Gray Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Red Red Brown Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Purple Purple Purple Yellow Green Green Green Green Green Green Green Yellow Yellow Gray Gray Gray Yellow Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Purple Yellow Purple Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Black Yellow Green Green Green Green Yellow
Row 20: Yellow Yellow Purple Purple Purple Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Yellow Green Yellow Yellow Green Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Green Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Orange Orange Orange Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Orange Orange Orange Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Orange Orange Orange Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Red Red Red Red Red Red Purple Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Red Red Red Red Red Red Purple Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Purple Red Red Red Red Purple Yellow Yellow Yellow Yellow Yellow Purple Red Red Red Red Red Red Purple Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Purple Red Red Red Red Purple Yellow Yellow Yellow Yellow Yellow Purple Red Red Red Red Red Red Purple Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Purple Red Red Red Red Purple Yellow Yellow Yellow Yellow Yellow Purple Red Red Red Red Red Red Purple Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Purple Red Red Red Red Purple Yellow Yellow Yellow Yellow Yellow Purple Red Red Red Red Red Red Purple Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Orange Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Purple Purple Purple Yellow Green Green Green Green Green Green Green Yellow Yellow Gray Gray Gray Yellow Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Purple Orange Purple Yellow Green Orange Orange Orange Orange Orange Green Yellow Yellow Yellow Yellow Yellow Yellow Black Orange Black Yellow Green Green Green Green Yellow
Row 20: Yellow Yellow Purple Purple Purple Yellow Green Orange Orange Orange Orange Orange Green Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Yellow Green Red Red Green Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Green Orange Orange Orange Orange Orange Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Red Red Green Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Green Orange Orange Orange Orange Orange Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Green Orange Orange Orange Orange Orange Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Blue Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Green Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Blue Blue Blue Pink Pink Black Black Black Black Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Blue Pink Blue Pink Pink Black Pink Pink Black Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Blue Blue Blue Pink Pink Black Pink Pink Black Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Black Black Black Black Pink Pink Pink Pink Pink
Row 13: Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Yellow Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Black Black Black Pink Pink Pink
Row 15: Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Black Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Black Black Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Blue Orange Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Orange Green Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Blue Blue Blue Pink Pink Black Black Black Black Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Blue Orange Blue Pink Pink Black Red Red Black Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Blue Blue Blue Pink Pink Black Red Red Black Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Black Black Black Black Pink Pink Pink Pink Pink
Row 13: Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Yellow Orange Yellow Pink Pink Pink Pink Pink Pink Pink Pink Black Black Black Pink Pink Pink
Row 15: Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Black Orange Black Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Black Black Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Green Pink Pink Pink Green Pink Pink Pink Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Green Pink Pink Pink Green Pink Pink Pink Brown Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Green Green Green Green Green Pink Pink Pink Brown Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Green Green Green Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Green Pink
Row 19: Pink Pink Pink Pink Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Green Pink
Row 20: Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Green Pink
Row 21: Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Green Pink
Row 22: Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Green Pink
Row 23: Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Green Pink
Row 24: Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Green Green Green Green Green Green Green Green Pink
Row 25: Pink Pink Pink Pink Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Green Orange Orange Orange Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Green Orange Orange Orange Green Pink Pink Pink Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Green Orange Orange Orange Green Pink Pink Pink Brown Red Red Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Green Green Green Green Green Pink Pink Pink Brown Red Red Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Green Green Green Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Red Red Red Red Red Red Green Pink
Row 19: Pink Pink Pink Pink Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Green Red Red Red Red Red Red Green Pink
Row 20: Pink Pink Pink Pink Gray Orange Orange Orange Orange Orange Gray Pink Pink Pink Pink Green Red Red Red Red Red Red Green Pink
Row 21: Pink Pink Pink Pink Gray Orange Orange Orange Orange Orange Gray Pink Pink Pink Pink Green Red Red Red Red Red Red Green Pink
Row 22: Pink Pink Pink Pink Gray Orange Orange Orange Orange Orange Gray Pink Pink Pink Pink Green Red Red Red Red Red Red Green Pink
Row 23: Pink Pink Pink Pink Gray Orange Orange Orange Orange Orange Gray Pink Pink Pink Pink Green Red Red Red Red Red Red Green Pink
Row 24: Pink Pink Pink Pink Gray Orange Orange Orange Orange Orange Gray Pink Pink Pink Pink Green Green Green Green Green Green Green Green Pink
Row 25: Pink Pink Pink Pink Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Pink Pink Pink Blue Blue
Row 3: Yellow Yellow Yellow Blue Blue Blue Pink Blue Pink Blue Blue
Row 4: Yellow Blue Yellow Blue Blue Blue Pink Pink Pink Blue Blue
Row 5: Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Blue
Row 7: Blue Blue Blue Blue Gray Blue Blue Blue Blue Gray Blue
Row 8: Blue Blue Blue Blue Gray Blue Blue Blue Blue Gray Blue
Row 9: Blue Blue Blue Blue Gray Blue Blue Blue Blue Gray Blue
Row 10: Pink Pink Pink Blue Gray Blue Blue Blue Blue Gray Blue
Row 11: Pink Blue Pink Blue Gray Gray Gray Gray Gray Gray Blue
Row 12: Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Blue
Row 18: Blue Blue Blue Brown Blue Blue Blue Blue Blue Brown Blue
Row 19: Blue Blue Blue Brown Blue Blue Blue Blue Blue Brown Blue
Row 20: Blue Blue Blue Brown Blue Blue Blue Blue Blue Brown Blue
Row 21: Blue Blue Blue Brown Blue Blue Blue Blue Blue Brown Blue
Row 22: Blue Blue Blue Brown Blue Blue Blue Blue Blue Brown Blue
Row 23: Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Blue
Row 24: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 26: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 27: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 28: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Pink Pink Pink Blue Blue
Yellow Yellow Yellow Blue Blue Blue Pink Orange Pink Blue Blue
Yellow Orange Yellow Blue Blue Blue Pink Pink Pink Blue Blue
Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Blue
Blue Blue Blue Blue Gray Red Red Red Red Gray Blue
Blue Blue Blue Blue Gray Red Red Red Red Gray Blue
Blue Blue Blue Blue Gray Red Red Red Red Gray Blue
Pink Pink Pink Blue Gray Red Red Red Red Gray Blue
Pink Orange Pink Blue Gray Gray Gray Gray Gray Gray Blue
Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Blue
Blue Blue Blue Brown Orange Orange Orange Orange Orange Brown Blue
Blue Blue Blue Brown Orange Orange Orange Orange Orange Brown Blue
Blue Blue Blue Brown Orange Orange Orange Orange Orange Brown Blue
Blue Blue Blue Brown Orange Orange Orange Orange Orange Brown Blue
Blue Blue Blue Brown Orange Orange Orange Orange Orange Brown Blue
Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Black Black Purple Brown Red
Row 2: Black Black Black Black Black Brown Black
Row 3: Black Black Black Black Black Green Brown
Row 4: Black Black Brown Black Black Black Red
Row 5: Black Black Brown Gray Black Black Black
Row 6: Gray Green Pink Pink Black Black Black
Row 7: Black Black Black Pink Black Black Black
Row 8: Black Black Black Black Purple Green Purple
Row 9: Black Black Black Black Black Purple Purple
Row 10: Black Black Black Black Black Purple Green
Row 11: Black Black Black Black Black Purple Red
Row 12: Green Purple Brown Red Green Black Black
Row 13: Black Pink Black Black Black Red Brown
Row 14: Black Black Black Black Pink Brown Purple
Row 15: Black Black Black Orange Brown Green Purple
Row 16: Black Black Black Gray Gray Black Brown
Row 17: Orange Black Pink Pink Black Black Red
Row 18: Pink Gray Purple Black Brown Black Red
Row 19: Pink Gray Orange Brown Black Black Gray
Row 20: Green Orange Red Pink Black Green Pink
Row 21: Purple Brown Black Black Black Black Brown
Row 22: Black Black Black Black Black Orange Black
Row 23: Black Black Black Black Black Gray Gray
Row 24: Black Black Black Black Black Black Brown
Row 25: Brown Black Black Black Black Pink Pink
Row 26: Orange Black Black Black Gray Pink Brown
Output:
Row 1: Blue Blue Blue Blue Purple Brown Red
Row 2: Blue Blue Blue Blue Black Brown Black
Row 3: Blue Blue Blue Blue Black Green Brown
Row 4: Black Black Brown Black Black Black Red
Row 5: Black Black Brown Gray Blue Blue Blue
Row 6: Gray Green Pink Pink Blue Blue Blue
Row 7: Blue Blue Blue Pink Blue Blue Blue
Row 8: Blue Blue Blue Blue Purple Green Purple
Row 9: Blue Blue Blue Blue Blue Purple Purple
Row 10: Blue Blue Blue Blue Blue Purple Green
Row 11: Blue Blue Blue Blue Blue Purple Red
Row 12: Green Purple Brown Red Green Black Black
Row 13: Black Pink Black Black Black Red Brown
Row 14: Blue Blue Blue Black Pink Brown Purple
Row 15: Blue Blue Blue Orange Brown Green Purple
Row 16: Blue Blue Blue Gray Gray Black Brown
Row 17: Orange Black Pink Pink Black Black Red
Row 18: Pink Gray Purple Black Brown Black Red
Row 19: Pink Gray Orange Brown Black Black Gray
Row 20: Green Orange Red Pink Black Green Pink
Row 21: Purple Brown Blue Blue Blue Black Brown
Row 22: Blue Blue Blue Blue Blue Orange Black
Row 23: Blue Blue Blue Blue Blue Gray Gray
Row 24: Blue Blue Blue Blue Blue Black Brown
Row 25: Brown Blue Blue Blue Blue Pink Pink
Row 26: Orange Blue Blue Blue Gray Pink Brown
Example 2
Input:
Row 1: Black Gray Purple Black Purple Red
Row 2: Gray Pink Black Yellow Red Purple
Row 3: Yellow Brown Black Purple Red Black
Row 4: Red Black Pink Black Green Yellow
Row 5: Gray Black Black Black Yellow Red
Row 6: Yellow Black Black Black Black Pink
Row 7: Black Black Black Black Black Black
Row 8: Green Brown Red Black Black Black
Row 9: Black Brown Black Black Black Black
Row 10: Black Yellow Black Black Black Black
Row 11: Pink Green Black Black Black Black
Row 12: Black Black Black Black Black Black
Row 13: Black Black Yellow Red Black Black
Row 14: Green Black Black Black Gray Red
Output:
Row 1: Black Gray Purple Black Purple Red
Row 2: Gray Pink Black Yellow Red Purple
Row 3: Yellow Brown Black Purple Red Black
Row 4: Red Black Pink Black Green Yellow
Row 5: Gray Blue Blue Blue Yellow Red
Row 6: Yellow Blue Blue Blue Black Pink
Row 7: Black Blue Blue Blue Blue Blue
Row 8: Green Brown Red Blue Blue Blue
Row 9: Black Brown Blue Blue Blue Blue
Row 10: Black Yellow Blue Blue Blue Blue
Row 11: Pink Green Blue Blue Blue Blue
Row 12: Black Black Blue Blue Blue Blue
Row 13: Black Black Yellow Red Black Black
Row 14: Green Black Black Black Gray Red
Example 3
Input:
Row 1: Black Orange Brown Purple Gray Black Orange Black Gray Gray Green Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Green Orange Gray Orange Green Black Yellow Black Purple Black Black Black Black Black Black Black Black Black Green
Row 3: Purple Brown Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange
Row 4: Brown Purple Black Purple Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Green
Row 5: Gray Orange Purple Black Black Black Black Black Black Black Black Black Black Black Yellow Black Black Black Black Black Gray
Row 6: Gray Black Orange Brown Black Black Yellow Black Black Black Black Black Purple Black Purple Purple Black Black Black Black Black
Row 7: Gray Black Black Black Black Orange Yellow Green Black Orange Black Black Black Brown Brown Black Black Black Black Black Black
Row 8: Black Black Black Black Brown Black Yellow Purple Black Black Green Purple Black Green Brown Brown Purple Orange Black Yellow Black
Row 9: Purple Black Black Black Black Black Orange Gray Yellow Brown Black Black Black Black Orange Yellow Brown Black Yellow Black Black
Row 10: Black Black Black Purple Black Black Black Yellow Orange Purple Black Black Black Brown Yellow Brown Orange Orange Orange Black Green
Row 11: Gray Orange Black Yellow Black Black Black Black Yellow Black Gray Gray Orange Black Black Brown Black Purple Gray Gray Yellow
Row 12: Black Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Yellow Yellow Black
Row 13: Orange Black Black Black Black Black Black Black Black Black Black Yellow Black Black Black Black Orange Black Orange Brown Black
Row 14: Brown Black Black Black Black Black Black Green Black Black Black Black Purple Black Black Black Gray Purple Yellow Black Gray
Row 15: Black Brown Black Black Black Black Black Purple Black Black Black Black Purple Orange Black Black Black Black Black Black Gray
Row 16: Purple Green Black Green Green Green Purple Black Black Black Black Black Black Yellow Black Black Black Black Purple Purple Orange
Row 17: Yellow Yellow Black Black Black Black Black Yellow Black Black Black Black Black Black Black Black Black Black Yellow Black Black
Row 18: Brown Black Black Green Purple Yellow Purple Purple Orange Green Green Black Purple Black Black Yellow Black Yellow Gray Green Purple
Row 19: Yellow Black Yellow Black Black Brown Orange Black Orange Purple Yellow Black Black Orange Orange Black Brown Black Black Purple Yellow
Output:
Row 1: Black Orange Brown Purple Gray Black Orange Black Gray Gray Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 2: Black Black Green Orange Gray Orange Green Black Yellow Black Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Green
Row 3: Purple Brown Gray Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange
Row 4: Brown Purple Black Purple Black Black Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green
Row 5: Gray Orange Purple Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Gray
Row 6: Gray Black Orange Brown Black Black Yellow Blue Blue Blue Blue Blue Purple Black Purple Purple Blue Blue Blue Blue Black
Row 7: Gray Blue Blue Blue Black Orange Yellow Green Black Orange Black Black Black Brown Brown Black Blue Blue Blue Blue Black
Row 8: Black Blue Blue Blue Brown Black Yellow Purple Black Black Green Purple Black Green Brown Brown Purple Orange Black Yellow Black
Row 9: Purple Blue Blue Blue Black Black Orange Gray Yellow Brown Black Black Black Black Orange Yellow Brown Black Yellow Black Black
Row 10: Black Black Black Purple Blue Blue Blue Yellow Orange Purple Black Black Black Brown Yellow Brown Orange Orange Orange Black Green
Row 11: Gray Orange Black Yellow Blue Blue Blue Blue Yellow Black Gray Gray Orange Black Black Brown Black Purple Gray Gray Yellow
Row 12: Black Blue Blue Blue Blue Blue Blue Blue Black Black Orange Black Black Blue Blue Blue Black Black Yellow Yellow Black
Row 13: Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Black Blue Blue Blue Orange Black Orange Brown Black
Row 14: Brown Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Purple Blue Blue Blue Gray Purple Yellow Black Gray
Row 15: Black Brown Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Purple Orange Blue Blue Blue Blue Black Black Gray
Row 16: Purple Green Black Green Green Green Purple Black Blue Blue Blue Blue Black Yellow Blue Blue Blue Blue Purple Purple Orange
Row 17: Yellow Yellow Black Black Black Black Black Yellow Blue Blue Blue Blue Black Black Blue Blue Blue Blue Yellow Black Black
Row 18: Brown Black Black Green Purple Yellow Purple Purple Orange Green Green Black Purple Black Black Yellow Black Yellow Gray Green Purple
Row 19: Yellow Black Yellow Black Black Brown Orange Black Orange Purple Yellow Black Black Orange Orange Black Brown Black Black Purple Yellow
Here is the input grid for the test example:
Input:
Row 1: Black Brown Brown Brown Black Black Yellow Brown Yellow Brown
Row 2: Black Black Black Black Black Black Brown Yellow Brown Black
Row 3: Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Yellow Yellow Black Yellow Brown
Row 5: Black Black Black Black Black Yellow Yellow Yellow Brown Black
Row 6: Black Black Black Black Black Black Brown Yellow Black Black
Row 7: Yellow Black Black Black Yellow Black Brown Brown Brown Black
Row 8: Brown Black Yellow Yellow Black Yellow Black Black Black Black
Row 9: Black Brown Black Black Brown Yellow Yellow Black Black Black
Row 10: Black Black Black Yellow Brown Brown Black Black Black Black
Row 11: Brown Black Black Black Black Brown Yellow Black Black Black
Row 12: Brown Brown Black Black Black Black Yellow Black Black Yellow
Row 13: Yellow Black Yellow Black Black Black Brown Black Yellow Yellow
Row 14: Yellow Black Black Black Black Black Black Black Black Brown
Row 15: Black Black Black Black Yellow Black Black Black Black Black
Row 16: Yellow Black Black Yellow Brown Black Black Black Black Black
Row 17: Black Black Black Black Black Brown Black Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Brown Brown Brown Black Black Yellow Brown Yellow Brown
Blue Blue Blue Blue Blue Black Brown Yellow Brown Black
Blue Blue Blue Blue Blue Black Black Black Black Black
Blue Blue Blue Blue Blue Yellow Yellow Black Yellow Brown
Blue Blue Blue Blue Blue Yellow Yellow Yellow Brown Black
Blue Blue Blue Blue Blue Black Brown Yellow Black Black
Yellow Blue Blue Blue Yellow Black Brown Brown Brown Black
Brown Black Yellow Yellow Black Yellow Black Blue Blue Blue
Black Brown Black Black Brown Yellow Yellow Blue Blue Blue
Black Black Black Yellow Brown Brown Black Blue Blue Blue
Brown Black Black Black Black Brown Yellow Blue Blue Blue
Brown Brown Black Blue Blue Blue Yellow Black Black Yellow
Yellow Black Yellow Blue Blue Blue Brown Black Yellow Yellow
Yellow Black Black Blue Blue Blue Blue Blue Blue Brown
Black Black Black Black Yellow Blue Blue Blue Blue Blue
Yellow Black Black Yellow Brown Blue Blue Blue Blue Blue
Black Black Black Black Black Brown Blue Blue Blue Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Purple Purple Purple Purple Purple Purple Purple Blue Purple Blue
Row 6: Purple Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 8: Purple Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 10: Blue Purple Purple Blue Purple Blue Purple Blue Purple Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 21: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Purple Purple Purple Purple Purple Purple Purple Red Purple Blue
Row 6: Purple Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 7: Red Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 8: Purple Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 9: Red Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 10: Red Purple Purple Red Purple Red Purple Red Purple Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 21: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Example 2
Input:
Row 1: Purple Purple Blue Blue Blue Purple Blue Purple Blue Purple Blue Purple Purple Blue Purple Purple Blue Purple Purple Purple Blue Purple Purple Blue Purple Purple Blue Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 3: Purple Purple Blue Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 5: Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 7: Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Blue Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Blue Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Blue Purple Purple Purple Purple Blue Blue Blue Purple Purple Purple Purple Purple Purple Blue Purple Blue Blue Blue Blue Blue Purple Blue Purple Blue Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 27: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Blue Blue Blue Red Blue Red Blue Red Blue Red Red Blue Red Red Blue Red Red Red Blue Red Red Blue Red Red Blue Purple
Row 2: Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 3: Purple Purple Blue Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple
Row 4: Purple Purple Blue Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 5: Purple Purple Blue Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple
Row 6: Purple Purple Red Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 7: Purple Purple Blue Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple
Row 8: Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple
Row 9: Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple
Row 10: Purple Purple Blue Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple
Row 11: Purple Purple Blue Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple
Row 12: Purple Purple Blue Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple
Row 13: Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple
Row 14: Purple Purple Blue Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 15: Purple Purple Red Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 16: Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 17: Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 18: Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 19: Purple Purple Red Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple
Row 20: Purple Purple Red Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple
Row 21: Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple
Row 22: Purple Purple Blue Red Red Red Red Blue Blue Blue Red Red Red Red Red Red Blue Red Blue Blue Blue Blue Blue Red Blue Red Blue Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 27: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange
Row 5: Green Green Green Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange
Row 6: Green Green Green Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange
Row 7: Green Green Green Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange
Row 8: Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange
Row 5: Green Green Green Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange
Row 6: Green Green Green Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange
Row 7: Green Green Green Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange
Row 8: Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Blue Blue Purple Blue Blue Blue Purple Purple Blue Blue Purple Blue Purple Purple Blue Blue Blue Purple Blue
Row 8: Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Blue
Row 9: Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Blue
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Blue Purple Purple Blue Blue Purple Purple Purple Blue Purple Purple Purple Blue Blue Purple Blue Blue Purple Blue
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Blue Blue Red Blue Blue Blue Red Red Blue Blue Red Blue Red Red Blue Blue Blue Red Blue
Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Blue
Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Red
Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Blue
Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Red
Purple Blue Red Red Blue Blue Red Red Red Blue Red Red Red Blue Blue Red Blue Blue Red Blue
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Red Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Red Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Red Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Red Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Red Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Red Blue Blue Blue
Row 10: Blue Blue Blue Blue Orange Red Red Blue Blue Blue
Row 11: Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Orange Blue Purple Purple Blue Blue
Row 14: Blue Blue Blue Blue Orange Orange Blue Purple Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Brown Brown Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue
Row 21: Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue
Row 22: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 26: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 27: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 28: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 29: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 30: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Brown Brown Purple Purple
Row 2: Brown Blue Blue Purple
Row 3: Brown Blue Blue Red
Row 4: Brown Blue Blue Red
Row 5: Orange Blue Blue Red
Row 6: Orange Blue Blue Red
Row 7: Orange Blue Blue Red
Row 8: Orange Blue Blue Red
Row 9: Orange Orange Red Red
Example 2
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Pink Pink Pink Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Pink Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Brown Brown Brown Brown Brown Brown Brown Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Purple Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Purple Purple Purple Purple Red Red Red Red
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Green Green Green Green
Row 2: Pink Red Red Red Red Red Red Red Red Red Green
Row 3: Brown Red Red Red Red Red Red Red Red Red Purple
Row 4: Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple
Example 3
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 28: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 29: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 30: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown
Row 2: Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown
Row 3: Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown
Row 4: Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown
Row 5: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown
Row 6: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown
Row 7: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown
Row 8: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple
Row 9: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple
Row 10: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple
Row 11: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple
Row 12: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple
Row 13: Red Red Red Red Red Red Purple Purple Purple Purple Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 27: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 28: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 29: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 30: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Gray Gray Gray Gray Red Red Red Red Red Red Red Red
Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black
Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Purple Purple Purple Red Red Red Red
Row 6: Red Red Red Red Red Purple Purple Purple Purple Purple Purple Red Red Red Red
Row 7: Red Red Red Red Red Purple Purple Purple Purple Red Purple Red Red Red Red
Row 8: Red Red Red Red Red Purple Purple Purple Purple Purple Purple Red Red Red Red
Row 9: Red Red Red Red Red Purple Purple Purple Purple Purple Purple Red Red Red Red
Row 10: Red Red Yellow Yellow Red Purple Purple Purple Purple Purple Purple Red Red Red Red
Row 11: Red Red Yellow Yellow Red Purple Purple Purple Purple Purple Purple Red Red Red Red
Row 12: Red Red Red Red Red Purple Purple Purple Purple Purple Purple Red Red Red Red
Row 13: Red Red Red Red Red Purple Purple Purple Red Purple Purple Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Purple Purple Purple Red Red Red Red Red
Row 6: Red Red Red Red Purple Purple Purple Purple Purple Purple Red Red Red Red Red
Row 7: Red Red Red Red Purple Purple Purple Purple Red Purple Red Red Red Red Red
Row 8: Red Red Red Red Purple Purple Purple Purple Purple Purple Red Red Red Red Red
Row 9: Red Red Red Red Purple Purple Purple Purple Purple Purple Red Red Red Red Red
Row 10: Red Red Yellow Yellow Purple Purple Purple Purple Purple Purple Red Red Red Red Red
Row 11: Red Red Yellow Yellow Purple Purple Purple Purple Purple Purple Red Red Red Red Red
Row 12: Red Red Red Red Purple Purple Purple Purple Purple Purple Red Red Red Red Red
Row 13: Red Red Red Red Purple Purple Purple Red Purple Purple Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Pink Black Black Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Pink Pink Pink Pink Pink Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Pink Black Pink Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Pink Pink Pink Pink Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Pink Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Pink Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Pink Black Black Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Pink Pink Pink Pink Pink Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Pink Black Pink Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Pink Pink Pink Pink Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Pink Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Pink Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Purple Purple
Row 8: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Purple Red Purple Purple
Row 9: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Purple Purple Purple
Row 10: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Purple Purple
Row 11: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Red Red Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Green Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Green Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Green Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Green Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Green Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Purple Purple Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Purple Purple Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Black Black Blue Black Black Brown Black Black
Row 2: Brown Black Blue Brown Blue Black Brown Black Black
Row 3: Black Black Blue Blue Black Blue Black Black Black
Row 4: Brown Blue Blue Black Brown Black Blue Black Black
Row 5: Blue Blue Brown Black Blue Black Blue Blue Black
Row 6: Brown Brown Brown Black Black Black Black Blue Blue
Row 7: Brown Blue Black Blue Black Blue Brown Brown Brown
Row 8: Blue Brown Blue Black Black Blue Black Black Black
Row 9: Brown Black Brown Black Black Black Black Black Blue
Row 10: Black Black Blue Black Black Blue Black Brown Blue
Row 11: Brown Brown Black Blue Black Black Black Blue Black
Row 12: Black Black Black Blue Black Blue Blue Black Black
Row 13: Brown Blue Black Black Brown Blue Blue Brown Brown
Row 14: Blue Black Black Black Blue Blue Black Brown Blue
Row 15: Blue Blue Blue Black Black Blue Brown Black Black
Row 16: Brown Blue Brown Blue Black Brown Black Blue Black
Row 17: Black Blue Blue Blue Blue Brown Brown Black Black
Row 18: Brown Brown Brown Brown Black Black Blue Brown Blue
Row 19: Black Black Black Black Black Black Brown Blue Black
Row 20: Black Blue Black Brown Blue Blue Blue Blue Black
Row 21: Black Blue Blue Black Black Brown Black Black Black
Row 22: Blue Black Black Brown Black Black Brown Blue Brown
Row 23: Black Blue Blue Black Blue Brown Black Brown Black
Row 24: Black Blue Blue Black Brown Brown Brown Black Blue
Row 25: Black Black Black Black Brown Brown Black Blue Black
Row 26: Blue Black Blue Blue Black Black Black Black Blue
Row 27: Brown Black Black Blue Blue Brown Black Brown Black
Row 28: Black Black Blue Blue Black Blue Black Black Brown
Row 29: Black Blue Brown Black Black Brown Blue Black Blue
Output:
Row 1: Blue Black Black Blue Black Black Brown Black Black Black Black Brown Black Black Blue Black Black Blue
Row 2: Brown Black Blue Brown Blue Black Brown Black Black Black Black Brown Black Blue Brown Blue Black Brown
Row 3: Black Black Blue Blue Black Blue Black Black Black Black Black Black Blue Black Blue Blue Black Black
Row 4: Brown Blue Blue Black Brown Black Blue Black Black Black Black Blue Black Brown Black Blue Blue Brown
Row 5: Blue Blue Brown Black Blue Black Blue Blue Black Black Blue Blue Black Blue Black Brown Blue Blue
Row 6: Brown Brown Brown Black Black Black Black Blue Blue Blue Blue Black Black Black Black Brown Brown Brown
Row 7: Brown Blue Black Blue Black Blue Brown Brown Brown Brown Brown Brown Blue Black Blue Black Blue Brown
Row 8: Blue Brown Blue Black Black Blue Black Black Black Black Black Black Blue Black Black Blue Brown Blue
Row 9: Brown Black Brown Black Black Black Black Black Blue Blue Black Black Black Black Black Brown Black Brown
Row 10: Black Black Blue Black Black Blue Black Brown Blue Blue Brown Black Blue Black Black Blue Black Black
Row 11: Brown Brown Black Blue Black Black Black Blue Black Black Blue Black Black Black Blue Black Brown Brown
Row 12: Black Black Black Blue Black Blue Blue Black Black Black Black Blue Blue Black Blue Black Black Black
Row 13: Brown Blue Black Black Brown Blue Blue Brown Brown Brown Brown Blue Blue Brown Black Black Blue Brown
Row 14: Blue Black Black Black Blue Blue Black Brown Blue Blue Brown Black Blue Blue Black Black Black Blue
Row 15: Blue Blue Blue Black Black Blue Brown Black Black Black Black Brown Blue Black Black Blue Blue Blue
Row 16: Brown Blue Brown Blue Black Brown Black Blue Black Black Blue Black Brown Black Blue Brown Blue Brown
Row 17: Black Blue Blue Blue Blue Brown Brown Black Black Black Black Brown Brown Blue Blue Blue Blue Black
Row 18: Brown Brown Brown Brown Black Black Blue Brown Blue Blue Brown Blue Black Black Brown Brown Brown Brown
Row 19: Black Black Black Black Black Black Brown Blue Black Black Blue Brown Black Black Black Black Black Black
Row 20: Black Blue Black Brown Blue Blue Blue Blue Black Black Blue Blue Blue Blue Brown Black Blue Black
Row 21: Black Blue Blue Black Black Brown Black Black Black Black Black Black Brown Black Black Blue Blue Black
Row 22: Blue Black Black Brown Black Black Brown Blue Brown Brown Blue Brown Black Black Brown Black Black Blue
Row 23: Black Blue Blue Black Blue Brown Black Brown Black Black Brown Black Brown Blue Black Blue Blue Black
Row 24: Black Blue Blue Black Brown Brown Brown Black Blue Blue Black Brown Brown Brown Black Blue Blue Black
Row 25: Black Black Black Black Brown Brown Black Blue Black Black Blue Black Brown Brown Black Black Black Black
Row 26: Blue Black Blue Blue Black Black Black Black Blue Blue Black Black Black Black Blue Blue Black Blue
Row 27: Brown Black Black Blue Blue Brown Black Brown Black Black Brown Black Brown Blue Blue Black Black Brown
Row 28: Black Black Blue Blue Black Blue Black Black Brown Brown Black Black Blue Black Blue Blue Black Black
Row 29: Black Blue Brown Black Black Brown Blue Black Blue Blue Black Blue Brown Black Black Brown Blue Black
Example 2
Input:
Row 1: Green Green
Row 2: Black Green
Row 3: Brown Green
Row 4: Brown Green
Row 5: Green Green
Row 6: Yellow Green
Row 7: Green Green
Row 8: Brown Green
Row 9: Brown Green
Row 10: Green Black
Row 11: Yellow Yellow
Row 12: Green Brown
Row 13: Green Brown
Row 14: Green Green
Row 15: Green Green
Row 16: Yellow Green
Row 17: Green Green
Row 18: Brown Green
Row 19: Green Brown
Row 20: Yellow Black
Row 21: Green Brown
Row 22: Green Green
Row 23: Yellow Black
Row 24: Green Green
Row 25: Green Green
Row 26: Black Green
Row 27: Yellow Yellow
Row 28: Green Green
Row 29: Yellow Green
Output:
Row 1: Green Green Green Green
Row 2: Black Green Green Black
Row 3: Brown Green Green Brown
Row 4: Brown Green Green Brown
Row 5: Green Green Green Green
Row 6: Yellow Green Green Yellow
Row 7: Green Green Green Green
Row 8: Brown Green Green Brown
Row 9: Brown Green Green Brown
Row 10: Green Black Black Green
Row 11: Yellow Yellow Yellow Yellow
Row 12: Green Brown Brown Green
Row 13: Green Brown Brown Green
Row 14: Green Green Green Green
Row 15: Green Green Green Green
Row 16: Yellow Green Green Yellow
Row 17: Green Green Green Green
Row 18: Brown Green Green Brown
Row 19: Green Brown Brown Green
Row 20: Yellow Black Black Yellow
Row 21: Green Brown Brown Green
Row 22: Green Green Green Green
Row 23: Yellow Black Black Yellow
Row 24: Green Green Green Green
Row 25: Green Green Green Green
Row 26: Black Green Green Black
Row 27: Yellow Yellow Yellow Yellow
Row 28: Green Green Green Green
Row 29: Yellow Green Green Yellow
Example 3
Input:
Row 1: Red Red Red Red Red Yellow Yellow Yellow Red Red Yellow Red
Row 2: Red Red Red Red Red Yellow Red Red Red Red Red Yellow
Row 3: Red Red Red Yellow Red Red Red Yellow Red Red Yellow Red
Row 4: Red Red Red Yellow Yellow Yellow Red Yellow Yellow Red Red Red
Row 5: Red Yellow Red Red Red Red Yellow Red Yellow Red Yellow Red
Row 6: Red Yellow Red Yellow Red Red Yellow Red Red Yellow Red Yellow
Row 7: Red Red Yellow Red Red Yellow Red Yellow Red Red Yellow Yellow
Row 8: Red Red Yellow Red Yellow Yellow Yellow Yellow Red Red Red Red
Row 9: Yellow Yellow Red Yellow Red Yellow Yellow Red Red Red Red Yellow
Row 10: Yellow Red Red Red Red Yellow Red Yellow Red Red Red Red
Row 11: Yellow Red Yellow Red Red Red Red Red Yellow Red Yellow Yellow
Row 12: Yellow Red Yellow Yellow Red Red Yellow Yellow Yellow Red Red Red
Row 13: Red Red Yellow Red Red Red Yellow Yellow Red Red Red Yellow
Row 14: Yellow Yellow Red Red Red Red Yellow Red Red Yellow Red Red
Row 15: Yellow Yellow Red Yellow Red Yellow Yellow Red Red Yellow Red Red
Row 16: Yellow Yellow Red Yellow Red Yellow Red Red Yellow Red Red Yellow
Row 17: Red Yellow Red Red Red Red Red Red Yellow Red Yellow Red
Row 18: Red Red Red Yellow Yellow Red Yellow Yellow Yellow Red Red Yellow
Row 19: Red Red Yellow Red Red Yellow Yellow Red Yellow Red Red Red
Row 20: Yellow Yellow Red Red Red Red Red Yellow Yellow Yellow Red Red
Row 21: Yellow Red Yellow Yellow Red Yellow Red Yellow Red Red Red Yellow
Output:
Row 1: Red Red Red Red Red Yellow Yellow Yellow Red Red Yellow Red Red Yellow Red Red Yellow Yellow Yellow Red Red Red Red Red
Row 2: Red Red Red Red Red Yellow Red Red Red Red Red Yellow Yellow Red Red Red Red Red Yellow Red Red Red Red Red
Row 3: Red Red Red Yellow Red Red Red Yellow Red Red Yellow Red Red Yellow Red Red Yellow Red Red Red Yellow Red Red Red
Row 4: Red Red Red Yellow Yellow Yellow Red Yellow Yellow Red Red Red Red Red Red Yellow Yellow Red Yellow Yellow Yellow Red Red Red
Row 5: Red Yellow Red Red Red Red Yellow Red Yellow Red Yellow Red Red Yellow Red Yellow Red Yellow Red Red Red Red Yellow Red
Row 6: Red Yellow Red Yellow Red Red Yellow Red Red Yellow Red Yellow Yellow Red Yellow Red Red Yellow Red Red Yellow Red Yellow Red
Row 7: Red Red Yellow Red Red Yellow Red Yellow Red Red Yellow Yellow Yellow Yellow Red Red Yellow Red Yellow Red Red Yellow Red Red
Row 8: Red Red Yellow Red Yellow Yellow Yellow Yellow Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Red Yellow Red Red
Row 9: Yellow Yellow Red Yellow Red Yellow Yellow Red Red Red Red Yellow Yellow Red Red Red Red Yellow Yellow Red Yellow Red Yellow Yellow
Row 10: Yellow Red Red Red Red Yellow Red Yellow Red Red Red Red Red Red Red Red Yellow Red Yellow Red Red Red Red Yellow
Row 11: Yellow Red Yellow Red Red Red Red Red Yellow Red Yellow Yellow Yellow Yellow Red Yellow Red Red Red Red Red Yellow Red Yellow
Row 12: Yellow Red Yellow Yellow Red Red Yellow Yellow Yellow Red Red Red Red Red Red Yellow Yellow Yellow Red Red Yellow Yellow Red Yellow
Row 13: Red Red Yellow Red Red Red Yellow Yellow Red Red Red Yellow Yellow Red Red Red Yellow Yellow Red Red Red Yellow Red Red
Row 14: Yellow Yellow Red Red Red Red Yellow Red Red Yellow Red Red Red Red Yellow Red Red Yellow Red Red Red Red Yellow Yellow
Row 15: Yellow Yellow Red Yellow Red Yellow Yellow Red Red Yellow Red Red Red Red Yellow Red Red Yellow Yellow Red Yellow Red Yellow Yellow
Row 16: Yellow Yellow Red Yellow Red Yellow Red Red Yellow Red Red Yellow Yellow Red Red Yellow Red Red Yellow Red Yellow Red Yellow Yellow
Row 17: Red Yellow Red Red Red Red Red Red Yellow Red Yellow Red Red Yellow Red Yellow Red Red Red Red Red Red Yellow Red
Row 18: Red Red Red Yellow Yellow Red Yellow Yellow Yellow Red Red Yellow Yellow Red Red Yellow Yellow Yellow Red Yellow Yellow Red Red Red
Row 19: Red Red Yellow Red Red Yellow Yellow Red Yellow Red Red Red Red Red Red Yellow Red Yellow Yellow Red Red Yellow Red Red
Row 20: Yellow Yellow Red Red Red Red Red Yellow Yellow Yellow Red Red Red Red Yellow Yellow Yellow Red Red Red Red Red Yellow Yellow
Row 21: Yellow Red Yellow Yellow Red Yellow Red Yellow Red Red Red Yellow Yellow Red Red Red Yellow Red Yellow Red Yellow Yellow Red Yellow
Here is the input grid for the test example:
Input:
Row 1: Red Pink Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Pink Brown Brown Pink Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Pink Pink Pink Purple
Row 3: Purple Purple Purple Pink Pink Purple
Row 4: Purple Purple Pink Purple Pink Purple
Row 5: Purple Purple Purple Pink Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple
Row 7: Red Red Red Red Red Red
Row 8: Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Pink Pink Purple
Row 10: Purple Purple Purple Purple Pink Purple
Row 11: Purple Purple Pink Pink Pink Purple
Row 12: Purple Purple Purple Pink Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple
Row 14: Red Red Red Red Red Red
Row 15: Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Pink Pink Pink Purple
Row 17: Purple Purple Purple Pink Pink Purple
Row 18: Purple Purple Pink Pink Pink Purple
Row 19: Purple Purple Purple Pink Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Pink Pink Pink Purple
Row 3: Purple Purple Purple Pink Pink Purple
Row 4: Purple Purple Pink Red Pink Purple
Row 5: Purple Purple Purple Pink Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple
Row 7: Red Red Red Red Red Red
Row 8: Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Red Pink Pink Purple
Row 10: Purple Purple Purple Red Pink Purple
Row 11: Purple Purple Pink Pink Pink Purple
Row 12: Purple Purple Purple Pink Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple
Row 14: Red Red Red Red Red Red
Row 15: Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Pink Pink Pink Purple
Row 17: Purple Purple Purple Pink Pink Purple
Row 18: Purple Purple Pink Pink Pink Purple
Row 19: Purple Purple Purple Pink Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Red Red Red Red Red Yellow Red Red Red Red Red
Row 2: Red Brown Red Red Red Yellow Red Brown Brown Red Red
Row 3: Red Red Red Red Red Yellow Red Red Red Red Red
Row 4: Red Red Red Red Red Yellow Red Red Red Red Red
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Red Red Red Red Red Yellow Red Red Red Red Red
Row 7: Red Brown Brown Red Red Yellow Red Brown Brown Red Red
Row 8: Red Red Red Red Red Yellow Red Red Red Red Red
Row 9: Red Red Red Red Red Yellow Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Yellow Red Red Red Red Red
Row 2: Red Brown Yellow Red Red Yellow Red Brown Brown Red Red
Row 3: Red Red Red Red Red Yellow Red Red Red Red Red
Row 4: Red Red Red Red Red Yellow Red Red Red Red Red
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Red Red Red Red Red Yellow Red Red Red Red Red
Row 7: Red Brown Brown Red Red Yellow Red Brown Brown Red Red
Row 8: Red Red Red Red Red Yellow Red Red Red Red Red
Row 9: Red Red Red Red Red Yellow Red Red Red Red Red
Example 3
Input:
Row 1: Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 2: Yellow Green Green Yellow Blue Yellow Green Yellow Yellow
Row 3: Yellow Green Green Yellow Blue Yellow Green Green Yellow
Row 4: Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 2: Yellow Green Green Yellow Blue Yellow Green Blue Yellow
Row 3: Yellow Green Green Yellow Blue Yellow Green Green Yellow
Row 4: Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Purple Orange Orange Yellow Orange Orange Orange Purple Orange Orange
Row 4: Orange Orange Purple Orange Orange Orange Yellow Orange Orange Orange Purple Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Purple Orange Orange Yellow Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Purple Purple Orange Orange Yellow Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange
Orange Orange Orange Purple Orange Orange Yellow Orange Orange Orange Purple Orange Orange
Orange Orange Purple Yellow Orange Orange Yellow Orange Orange Yellow Purple Orange Orange
Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange
Orange Orange Orange Purple Orange Orange Yellow Orange Orange Orange Yellow Orange Orange
Orange Orange Purple Purple Orange Orange Yellow Orange Orange Yellow Yellow Orange Orange
Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Gray Yellow Pink Purple Purple Purple Blue Pink Purple Purple Yellow Gray Purple Yellow Red Blue Yellow Purple Pink Red
Row 2: Purple Purple Purple Purple Yellow Purple Red Gray Purple Red Gray Purple Purple Blue Blue Purple Pink Purple Gray Gray Red
Row 3: Blue Pink Purple Purple Purple Pink Purple Yellow Pink Purple Purple Pink Purple Purple Red Red Purple Purple Blue Purple Pink
Row 4: Red Purple Red Purple Purple Purple Blue Red Gray Blue Purple Purple Red Red Purple Yellow Yellow Pink Purple Blue Yellow
Row 5: Red Pink Gray Red Purple Pink Gray Purple Blue Blue Yellow Red Purple Yellow Purple Purple Gray Purple Purple Purple Yellow
Row 6: Pink Purple Purple Yellow Red Purple Yellow Purple Purple Red Pink Purple Purple Pink Purple Pink Purple Purple Purple Purple Gray
Row 7: Gray Purple Purple Purple Purple Red Red Gray Purple Purple Red Purple Purple Yellow Purple Red Pink Purple Purple Purple Purple
Row 8: Yellow Purple Purple Gray Purple Purple Purple Red Red Yellow Gray Purple Blue Blue Purple Red Purple Pink Red Red Yellow
Row 9: Purple Gray Pink Purple Purple Purple Blue Purple Gray Purple Purple Purple Blue Yellow Yellow Gray Purple Purple Purple Gray Yellow
Row 10: Red Yellow Gray Purple Yellow Purple Purple Purple Gray Yellow Yellow Purple Gray Red Yellow Blue Blue Gray Blue Red Purple
Row 11: Purple Gray Purple Purple Purple Blue Yellow Yellow Gray Pink Purple Yellow Purple Purple Yellow Purple Purple Yellow Pink Red Pink
Row 12: Purple Pink Purple Purple Purple Pink Purple Yellow Pink Yellow Blue Blue Red Purple Purple Purple Gray Pink Gray Purple Purple
Row 13: Purple Red Yellow Yellow Purple Purple Red Pink Purple Red Gray Purple Yellow Red Red Red Yellow Purple Purple Gray Yellow
Row 14: Red Purple Gray Red Yellow Yellow Purple Purple Yellow Purple Red Gray Pink Yellow Yellow Blue Purple Gray Pink Purple Gray
Row 15: Gray Purple Gray Yellow Purple Yellow Purple Gray Blue Purple Yellow Pink Yellow Gray Yellow Red Yellow Red Purple Yellow Gray
Row 16: Purple Gray Yellow Pink Purple Purple Purple Blue Pink Purple Purple Yellow Gray Purple Yellow Red Blue Yellow Purple Pink Red
Row 17: Purple Purple Purple Purple Yellow Purple Red Gray Purple Red Gray Purple Purple Blue Blue Purple Pink Purple Gray Gray Red
Row 18: Blue Pink Purple Purple Purple Pink Purple Yellow Pink Purple Purple Pink Purple Purple Red Red Purple Purple Blue Purple Pink
Row 19: Red Purple Red Purple Purple Purple Blue Red Gray Blue Purple Purple Red Red Purple Yellow Yellow Pink Purple Blue Yellow
Row 20: Red Pink Gray Red Purple Pink Gray Purple Blue Blue Yellow Red Purple Yellow Purple Purple Gray Purple Purple Purple Yellow
Row 21: Pink Purple Purple Yellow Red Purple Yellow Purple Purple Red Pink Purple Purple Pink Purple Pink Purple Purple Purple Purple Gray
Row 22: Gray Purple Purple Purple Purple Red Red Gray Purple Purple Red Purple Purple Yellow Purple Red Pink Purple Purple Purple Purple
Row 23: Yellow Purple Purple Gray Purple Purple Purple Red Red Yellow Gray Purple Blue Blue Purple Red Purple Pink Red Red Yellow
Row 24: Purple Gray Pink Purple Purple Purple Blue Purple Gray Purple Purple Purple Blue Yellow Yellow Gray Purple Purple Purple Gray Yellow
Row 25: Red Yellow Gray Purple Yellow Purple Purple Purple Gray Yellow Yellow Purple Gray Red Yellow Blue Blue Gray Blue Red Purple
Row 26: Purple Gray Purple Purple Purple Blue Yellow Yellow Gray Pink Purple Yellow Purple Purple Yellow Purple Purple Yellow Pink Red Pink
Row 27: Purple Pink Purple Purple Purple Pink Purple Yellow Pink Yellow Blue Blue Red Purple Purple Purple Gray Pink Gray Purple Purple
Row 28: Purple Red Yellow Yellow Purple Purple Red Pink Purple Red Gray Purple Yellow Red Red Red Yellow Purple Purple Gray Yellow
Row 29: Red Purple Gray Red Yellow Yellow Purple Purple Yellow Purple Red Gray Pink Yellow Yellow Blue Purple Gray Pink Purple Gray
Row 30: Gray Purple Gray Yellow Purple Yellow Purple Gray Blue Purple Yellow Pink Yellow Gray Yellow Red Yellow Red Purple Yellow Gray
Output:
Row 1: Purple Gray Yellow Pink Purple Purple Purple Blue Pink Purple Purple Yellow Gray Purple Yellow Red Blue Yellow Purple Pink Red
Row 2: Purple Purple Purple Purple Yellow Purple Red Gray Purple Red Gray Purple Purple Blue Blue Purple Pink Purple Gray Gray Red
Row 3: Blue Pink Purple Purple Purple Pink Purple Yellow Pink Purple Purple Pink Purple Purple Red Red Purple Purple Blue Purple Pink
Row 4: Red Purple Red Purple Purple Purple Blue Red Gray Blue Purple Purple Red Red Purple Yellow Yellow Pink Purple Blue Yellow
Row 5: Red Pink Gray Red Purple Pink Gray Purple Blue Blue Yellow Red Purple Yellow Purple Purple Gray Purple Purple Purple Yellow
Row 6: Pink Purple Purple Yellow Red Purple Yellow Purple Purple Red Pink Purple Purple Pink Purple Pink Purple Purple Purple Purple Gray
Row 7: Gray Purple Purple Purple Purple Red Red Gray Purple Purple Red Purple Purple Yellow Purple Red Pink Purple Purple Purple Purple
Row 8: Yellow Purple Purple Gray Purple Purple Purple Red Red Yellow Gray Purple Blue Blue Purple Red Purple Pink Red Red Yellow
Row 9: Purple Gray Pink Purple Purple Purple Blue Purple Gray Purple Purple Purple Blue Yellow Yellow Gray Purple Purple Purple Gray Yellow
Row 10: Red Yellow Gray Purple Yellow Purple Purple Purple Gray Yellow Yellow Purple Gray Red Yellow Blue Blue Gray Blue Red Purple
Row 11: Purple Gray Purple Purple Purple Blue Yellow Yellow Gray Pink Purple Yellow Purple Purple Yellow Purple Purple Yellow Pink Red Pink
Row 12: Purple Pink Purple Purple Purple Pink Purple Yellow Pink Yellow Blue Blue Red Purple Purple Purple Gray Pink Gray Purple Purple
Row 13: Purple Red Yellow Yellow Purple Purple Red Pink Purple Red Gray Purple Yellow Red Red Red Yellow Purple Purple Gray Yellow
Row 14: Red Purple Gray Red Yellow Yellow Purple Purple Yellow Purple Red Gray Pink Yellow Yellow Blue Purple Gray Pink Purple Gray
Row 15: Gray Purple Gray Yellow Purple Yellow Purple Gray Blue Purple Yellow Pink Yellow Gray Yellow Red Yellow Red Purple Yellow Gray
Example 2
Input:
Row 1: Brown Pink Pink Pink Yellow Pink Brown Pink Pink Yellow Pink Brown Pink Pink Pink Pink Yellow
Row 2: Pink Yellow Pink Yellow Pink Yellow Pink Pink Pink Yellow Brown Pink Black Pink Green Pink Pink
Row 3: Brown Pink Brown Yellow Green Pink Pink Pink Pink Pink Black Brown Pink Pink Pink Pink Yellow
Row 4: Brown Pink Pink Pink Yellow Pink Brown Pink Pink Yellow Pink Brown Pink Pink Pink Pink Yellow
Row 5: Pink Yellow Pink Yellow Pink Yellow Pink Pink Pink Yellow Brown Pink Black Pink Green Pink Pink
Row 6: Brown Pink Brown Yellow Green Pink Pink Pink Pink Pink Black Brown Pink Pink Pink Pink Yellow
Output:
Row 1: Brown Pink Pink Pink Yellow Pink Brown Pink Pink Yellow Pink Brown Pink Pink Pink Pink Yellow
Row 2: Pink Yellow Pink Yellow Pink Yellow Pink Pink Pink Yellow Brown Pink Black Pink Green Pink Pink
Row 3: Brown Pink Brown Yellow Green Pink Pink Pink Pink Pink Black Brown Pink Pink Pink Pink Yellow
Example 3
Input:
Row 1: Brown Pink Brown Pink Pink Orange Pink Brown Brown Orange Brown
Row 2: Brown Brown Pink Pink Brown Pink Brown Orange Brown Brown Pink
Row 3: Brown Pink Pink Brown Brown Brown Brown Orange Orange Pink Pink
Row 4: Brown Pink Brown Pink Pink Orange Pink Brown Brown Orange Brown
Row 5: Brown Brown Pink Pink Brown Pink Brown Orange Brown Brown Pink
Row 6: Brown Pink Pink Brown Brown Brown Brown Orange Orange Pink Pink
Output:
Row 1: Brown Pink Brown Pink Pink Orange Pink Brown Brown Orange Brown
Row 2: Brown Brown Pink Pink Brown Pink Brown Orange Brown Brown Pink
Row 3: Brown Pink Pink Brown Brown Brown Brown Orange Orange Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Pink Red Red Yellow Pink Pink Orange Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Blue Pink Black
Row 2: Gray Pink Pink Yellow Blue Pink Black Blue Yellow Pink Pink Pink Orange Pink Pink Pink Gray Pink Orange Orange
Row 3: Red Pink Blue Pink Red Pink Black Pink Orange Pink Blue Gray Red Gray Blue Gray Gray Blue Red Pink
Row 4: Pink Red Red Yellow Pink Pink Orange Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Blue Pink Black
Row 5: Gray Pink Pink Yellow Blue Pink Black Blue Yellow Pink Pink Pink Orange Pink Pink Pink Gray Pink Orange Orange
Row 6: Red Pink Blue Pink Red Pink Black Pink Orange Pink Blue Gray Red Gray Blue Gray Gray Blue Red Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Red Red Yellow Pink Pink Orange Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Blue Pink Black
Gray Pink Pink Yellow Blue Pink Black Blue Yellow Pink Pink Pink Orange Pink Pink Pink Gray Pink Orange Orange
Red Pink Blue Pink Red Pink Black Pink Orange Pink Blue Gray Red Gray Blue Gray Gray Blue Red Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Green Brown
Row 2: Green Brown Brown Brown Pink
Row 3: Black Brown Orange Blue Brown
Row 4: Brown Brown Purple Brown Black
Row 5: Brown Brown Yellow Brown Purple
Row 6: Orange Brown Pink Blue Red
Output:
Row 1: Brown Brown Brown Green Brown Brown Green Brown Brown Brown
Row 2: Green Brown Brown Brown Pink Pink Brown Brown Brown Green
Row 3: Black Brown Orange Blue Brown Brown Blue Orange Brown Black
Row 4: Brown Brown Purple Brown Black Black Brown Purple Brown Brown
Row 5: Brown Brown Yellow Brown Purple Purple Brown Yellow Brown Brown
Row 6: Orange Brown Pink Blue Red Red Blue Pink Brown Orange
Row 7: Orange Brown Pink Blue Red Red Blue Pink Brown Orange
Row 8: Brown Brown Yellow Brown Purple Purple Brown Yellow Brown Brown
Row 9: Brown Brown Purple Brown Black Black Brown Purple Brown Brown
Row 10: Black Brown Orange Blue Brown Brown Blue Orange Brown Black
Row 11: Green Brown Brown Brown Pink Pink Brown Brown Brown Green
Row 12: Brown Brown Brown Green Brown Brown Green Brown Brown Brown
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Example 3
Input:
Row 1: Orange Red Yellow
Row 2: Green Green Brown
Row 3: Brown Yellow Green
Row 4: Brown Green Brown
Row 5: Black Green Green
Row 6: Green Green Green
Row 7: Green Green Brown
Row 8: Red Red Green
Row 9: Green Green Green
Row 10: Green Green Yellow
Output:
Row 1: Orange Red Yellow Yellow Red Orange
Row 2: Green Green Brown Brown Green Green
Row 3: Brown Yellow Green Green Yellow Brown
Row 4: Brown Green Brown Brown Green Brown
Row 5: Black Green Green Green Green Black
Row 6: Green Green Green Green Green Green
Row 7: Green Green Brown Brown Green Green
Row 8: Red Red Green Green Red Red
Row 9: Green Green Green Green Green Green
Row 10: Green Green Yellow Yellow Green Green
Row 11: Green Green Yellow Yellow Green Green
Row 12: Green Green Green Green Green Green
Row 13: Red Red Green Green Red Red
Row 14: Green Green Brown Brown Green Green
Row 15: Green Green Green Green Green Green
Row 16: Black Green Green Green Green Black
Row 17: Brown Green Brown Brown Green Brown
Row 18: Brown Yellow Green Green Yellow Brown
Row 19: Green Green Brown Brown Green Green
Row 20: Orange Red Yellow Yellow Red Orange
Here is the input grid for the test example:
Input:
Row 1: Orange Gray Gray Gray Gray Gray Gray Black Green
Row 2: Purple Gray Black Gray Blue Yellow Gray Brown Purple
Row 3: Yellow Orange Orange Gray Gray Blue Black Gray Orange
Row 4: Brown Gray Gray Purple Orange Gray Orange Gray Gray
Row 5: Green Gray Gray Gray Pink Gray Yellow Gray Purple
Row 6: Gray Blue Gray Brown Gray Gray Pink Green Gray
Row 7: Purple Gray Gray Brown Yellow Gray Orange Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Orange Gray Blue
Row 9: Gray Blue Gray Brown Yellow Gray Blue Yellow Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Gray Gray Gray Gray Gray Gray Black Green Green Black Gray Gray Gray Gray Gray Gray Orange
Purple Gray Black Gray Blue Yellow Gray Brown Purple Purple Brown Gray Yellow Blue Gray Black Gray Purple
Yellow Orange Orange Gray Gray Blue Black Gray Orange Orange Gray Black Blue Gray Gray Orange Orange Yellow
Brown Gray Gray Purple Orange Gray Orange Gray Gray Gray Gray Orange Gray Orange Purple Gray Gray Brown
Green Gray Gray Gray Pink Gray Yellow Gray Purple Purple Gray Yellow Gray Pink Gray Gray Gray Green
Gray Blue Gray Brown Gray Gray Pink Green Gray Gray Green Pink Gray Gray Brown Gray Blue Gray
Purple Gray Gray Brown Yellow Gray Orange Gray Gray Gray Gray Orange Gray Yellow Brown Gray Gray Purple
Gray Gray Gray Gray Gray Gray Orange Gray Blue Blue Gray Orange Gray Gray Gray Gray Gray Gray
Gray Blue Gray Brown Yellow Gray Blue Yellow Blue Blue Yellow Blue Gray Yellow Brown Gray Blue Gray
Gray Blue Gray Brown Yellow Gray Blue Yellow Blue Blue Yellow Blue Gray Yellow Brown Gray Blue Gray
Gray Gray Gray Gray Gray Gray Orange Gray Blue Blue Gray Orange Gray Gray Gray Gray Gray Gray
Purple Gray Gray Brown Yellow Gray Orange Gray Gray Gray Gray Orange Gray Yellow Brown Gray Gray Purple
Gray Blue Gray Brown Gray Gray Pink Green Gray Gray Green Pink Gray Gray Brown Gray Blue Gray
Green Gray Gray Gray Pink Gray Yellow Gray Purple Purple Gray Yellow Gray Pink Gray Gray Gray Green
Brown Gray Gray Purple Orange Gray Orange Gray Gray Gray Gray Orange Gray Orange Purple Gray Gray Brown
Yellow Orange Orange Gray Gray Blue Black Gray Orange Orange Gray Black Blue Gray Gray Orange Orange Yellow
Purple Gray Black Gray Blue Yellow Gray Brown Purple Purple Brown Gray Yellow Blue Gray Black Gray Purple
Orange Gray Gray Gray Gray Gray Gray Black Green Green Black Gray Gray Gray Gray Gray Gray Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Red Red Brown Brown Red Red Red Red
Row 2: Red Red Red Red Purple Purple Purple Purple Purple Red
Row 3: Red Red Red Red Purple Purple Purple Purple Purple Red
Row 4: Red Red Red Red Purple Purple Purple Purple Purple Red
Row 5: Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Brown Brown
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray
Example 3
Input:
Row 1: Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green
Row 3: Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green
Row 4: Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green
Row 5: Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green
Row 6: Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green
Row 7: Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Orange Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Orange Gray Gray Blue Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Orange Gray Gray Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Green Green Green
Row 12: Orange Gray Gray Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Green Green Green
Row 13: Orange Gray Gray Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Green Green Green
Row 14: Orange Gray Gray Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Green Green Green
Row 15: Orange Gray Gray Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Purple Purple Green
Row 16: Orange Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Green
Row 17: Orange Orange Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Green
Row 18: Orange Orange Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Green
Row 19: Orange Orange Orange Orange Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Orange
Row 20: Orange Orange Orange Orange Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Orange
Row 21: Orange Orange Orange Orange Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Orange
Row 22: Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange
Row 23: Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange
Row 24: Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange
Row 25: Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange
Row 26: Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Red Red Red Red Gray Gray
Row 5: Gray Gray Gray Gray Red Red Red Red Gray Gray
Row 6: Gray Gray Gray Gray Red Red Red Red Gray Gray
Row 7: Gray Gray Gray Gray Red Red Red Red Gray Gray
Row 8: Gray Gray Gray Gray Red Red Red Red Gray Gray
Row 9: Gray Gray Gray Gray Red Red Red Red Gray Gray
Row 10: Gray Gray Gray Gray Red Red Red Red Gray Gray
Row 11: Gray Gray Gray Gray Red Red Red Red Gray Gray
Row 12: Gray Gray Gray Gray Red Red Red Red Gray Gray
Row 13: Gray Gray Gray Gray Red Red Red Red Gray Gray
Row 14: Gray Gray Gray Gray Red Red Red Red Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Red Red Red
Red Red Red Red
Red Red Red Red
Red Red Red Red
Red Red Red Red
Red Red Red Red
Red Red Red Red
Red Red Red Red
Red Red Red Red
Red Red Red Red
Red Red Red Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Blue Blue Blue Red Red
Row 3: Red Red Red Red Red Red Blue Blue Blue Red Red
Row 4: Red Red Red Red Red Red Blue Blue Blue Red Red
Row 5: Gray Gray Gray Gray Gray Red Blue Blue Blue Red Red
Row 6: Gray Gray Gray Gray Gray Red Blue Blue Blue Red Red
Row 7: Gray Gray Gray Gray Gray Red Blue Blue Blue Red Red
Row 8: Red Red Red Red Red Red Blue Blue Blue Red Red
Row 9: Red Red Red Red Red Red Blue Blue Blue Red Red
Row 10: Red Red Red Red Red Red Blue Blue Blue Red Red
Row 11: Red Red Red Red Red Red Blue Blue Blue Red Red
Row 12: Red Red Red Red Red Red Blue Blue Blue Red Red
Row 13: Red Red Red Red Red Red Blue Blue Blue Red Red
Row 14: Red Red Red Red Red Red Blue Blue Blue Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Purple Purple Purple Purple Purple Red
Row 21: Red Red Red Red Red Purple Purple Purple Purple Purple Red
Row 22: Red Red Red Red Red Purple Purple Purple Purple Purple Red
Row 23: Red Red Red Red Red Green Green Green Green Green Red
Row 24: Red Red Red Red Red Green Green Green Green Green Red
Row 25: Red Red Red Red Red Green Green Green Green Green Red
Row 26: Red Red Red Red Red Red Red Red Red Red Red
Row 27: Red Red Red Red Red Red Red Red Red Red Red
Row 28: Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Blue Blue Blue Red Red
Row 3: Red Red Red Red Red Red Blue Red Blue Red Red
Row 4: Red Red Red Red Red Red Blue Blue Blue Red Red
Row 5: Gray Gray Gray Gray Gray Red Blue Red Blue Red Red
Row 6: Gray Red Gray Red Gray Red Blue Blue Blue Red Red
Row 7: Gray Gray Gray Gray Gray Red Blue Red Blue Red Red
Row 8: Red Red Red Red Red Red Blue Blue Blue Red Red
Row 9: Red Red Red Red Red Red Blue Red Blue Red Red
Row 10: Red Red Red Red Red Red Blue Blue Blue Red Red
Row 11: Red Red Red Red Red Red Blue Red Blue Red Red
Row 12: Red Red Red Red Red Red Blue Blue Blue Red Red
Row 13: Red Red Red Red Red Red Blue Red Blue Red Red
Row 14: Red Red Red Red Red Red Blue Blue Blue Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Purple Purple Purple Purple Purple Red
Row 21: Red Red Red Red Red Purple Red Purple Red Purple Red
Row 22: Red Red Red Red Red Purple Purple Purple Purple Purple Red
Row 23: Red Red Red Red Red Green Green Green Green Green Red
Row 24: Red Red Red Red Red Green Red Green Red Green Red
Row 25: Red Red Red Red Red Green Green Green Green Green Red
Row 26: Red Red Red Red Red Red Red Red Red Red Red
Row 27: Red Red Red Red Red Red Red Red Red Red Red
Row 28: Red Red Red Red Red Red Red Red Red Red Red
Example 2
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray
Row 6: Pink Gray Pink Gray Pink Gray Pink Gray Pink Gray Pink Gray Pink Gray Pink Gray Pink Gray Pink Gray Gray
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Brown Gray Brown Gray Brown Gray Brown Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Pink Pink Pink Purple Purple Purple Purple
Row 4: Purple Purple Purple Pink Pink Pink Purple Purple Purple Purple
Row 5: Purple Purple Purple Pink Pink Pink Purple Purple Purple Purple
Row 6: Purple Purple Purple Pink Pink Pink Orange Orange Orange Purple
Row 7: Purple Purple Purple Pink Pink Pink Orange Orange Orange Purple
Row 8: Purple Purple Purple Pink Pink Pink Orange Orange Orange Purple
Row 9: Purple Purple Purple Pink Pink Pink Orange Orange Orange Purple
Row 10: Purple Purple Purple Pink Pink Pink Orange Orange Orange Purple
Row 11: Purple Purple Purple Pink Pink Pink Orange Orange Orange Purple
Row 12: Purple Purple Purple Pink Pink Pink Orange Orange Orange Purple
Row 13: Purple Purple Purple Pink Pink Pink Orange Orange Orange Purple
Row 14: Purple Purple Purple Pink Pink Pink Orange Orange Orange Purple
Row 15: Purple Purple Purple Pink Pink Pink Orange Orange Orange Purple
Row 16: Purple Purple Purple Pink Pink Pink Orange Orange Orange Purple
Row 17: Purple Purple Purple Pink Pink Pink Orange Orange Orange Purple
Row 18: Purple Purple Purple Pink Pink Pink Orange Orange Orange Purple
Row 19: Purple Purple Purple Pink Pink Pink Orange Orange Orange Purple
Row 20: Purple Purple Purple Pink Pink Pink Orange Orange Orange Purple
Row 21: Purple Purple Purple Pink Pink Pink Orange Orange Orange Purple
Row 22: Purple Purple Purple Pink Pink Pink Orange Orange Orange Purple
Row 23: Purple Purple Purple Pink Pink Pink Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Pink Pink Pink Purple Purple Purple Purple
Row 4: Purple Purple Purple Pink Purple Pink Purple Purple Purple Purple
Row 5: Purple Purple Purple Pink Pink Pink Purple Purple Purple Purple
Row 6: Purple Purple Purple Pink Purple Pink Orange Orange Orange Purple
Row 7: Purple Purple Purple Pink Pink Pink Orange Purple Orange Purple
Row 8: Purple Purple Purple Pink Purple Pink Orange Orange Orange Purple
Row 9: Purple Purple Purple Pink Pink Pink Orange Purple Orange Purple
Row 10: Purple Purple Purple Pink Purple Pink Orange Orange Orange Purple
Row 11: Purple Purple Purple Pink Pink Pink Orange Purple Orange Purple
Row 12: Purple Purple Purple Pink Purple Pink Orange Orange Orange Purple
Row 13: Purple Purple Purple Pink Pink Pink Orange Purple Orange Purple
Row 14: Purple Purple Purple Pink Purple Pink Orange Orange Orange Purple
Row 15: Purple Purple Purple Pink Pink Pink Orange Purple Orange Purple
Row 16: Purple Purple Purple Pink Purple Pink Orange Orange Orange Purple
Row 17: Purple Purple Purple Pink Pink Pink Orange Purple Orange Purple
Row 18: Purple Purple Purple Pink Purple Pink Orange Orange Orange Purple
Row 19: Purple Purple Purple Pink Pink Pink Orange Purple Orange Purple
Row 20: Purple Purple Purple Pink Purple Pink Orange Orange Orange Purple
Row 21: Purple Purple Purple Pink Pink Pink Orange Purple Orange Purple
Row 22: Purple Purple Purple Pink Purple Pink Orange Orange Orange Purple
Row 23: Purple Purple Purple Pink Pink Pink Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Green Green Green Green Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green
Row 2: Green Green Green Green Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green
Row 3: Green Green Green Green Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green
Row 4: Green Green Green Green Orange Orange Orange Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green
Row 5: Green Green Green Green Orange Orange Orange Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green
Row 6: Green Green Green Green Orange Orange Orange Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green
Row 7: Green Green Green Green Orange Orange Orange Green Green Purple Purple Purple Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Orange Orange Orange Green Green Purple Purple Purple Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Orange Orange Orange Green Green Purple Purple Purple Green Green Green Green Green Green Red Red Red Green Green Green Green
Row 10: Green Green Green Green Orange Orange Orange Green Green Purple Purple Purple Green Green Green Green Green Green Red Red Red Green Green Green Green
Row 11: Green Green Green Green Orange Orange Orange Green Green Purple Purple Purple Green Green Green Green Green Green Red Red Red Green Green Green Green
Row 12: Brown Brown Brown Green Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Brown Brown Brown Green Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Brown Brown Brown Green Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Brown Brown Brown Green Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Brown Brown Brown Green Orange Orange Orange Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green
Row 17: Brown Brown Brown Green Orange Orange Orange Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green
Row 18: Brown Brown Brown Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Green Green Green Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green
Green Green Green Green Orange Green Orange Gray Green Gray Green Gray Green Gray Green Gray Green Gray Green Gray Green Gray Green Gray Green
Green Green Green Green Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green
Green Green Green Green Orange Green Orange Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green
Green Green Green Green Orange Orange Orange Green Blue Green Blue Green Blue Green Blue Green Blue Green Blue Green Blue Green Blue Green Green
Green Green Green Green Orange Green Orange Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green
Green Green Green Green Orange Orange Orange Green Green Purple Purple Purple Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Orange Green Orange Green Green Purple Green Purple Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Orange Orange Orange Green Green Purple Purple Purple Green Green Green Green Green Green Red Red Red Green Green Green Green
Green Green Green Green Orange Green Orange Green Green Purple Green Purple Green Green Green Green Green Green Red Green Red Green Green Green Green
Green Green Green Green Orange Orange Orange Green Green Purple Purple Purple Green Green Green Green Green Green Red Red Red Green Green Green Green
Brown Brown Brown Green Orange Green Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Brown Green Brown Green Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Brown Brown Brown Green Orange Green Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Brown Green Brown Green Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Brown Brown Brown Green Orange Green Orange Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green
Brown Green Brown Green Orange Orange Orange Green Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green
Brown Brown Brown Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black Black Brown Black Black Black Black Brown Black Black Black Black
Row 3: Black Black Brown Black Black Black Black Brown Black Black Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Brown Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Brown Black Black Black Black
Row 6: Black Black Black Brown Black Black Brown Black Black Brown Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Brown Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black
Row 9: Black Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black Black Brown Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black Black
Row 13: Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black
Row 15: Black Black Black Black Black Brown Black Black Black Black Black Black Brown Black Black Black Brown Black Black Black Brown Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Brown Blue Brown Black Black Black Black Black Brown Blue Brown Black Black Brown Blue Brown Black Black Black
Row 2: Black Brown Blue Brown Black Black Brown Blue Brown Blue Black Blue Brown Blue Brown Black Black Blue Black Blue Black Black Blue Black Blue Brown Blue Brown
Row 3: Black Blue Black Blue Black Black Blue Black Blue Brown Blue Brown Blue Black Blue Black Black Brown Blue Brown Black Black Brown Blue Brown Blue Black Blue
Row 4: Black Brown Blue Brown Black Black Brown Blue Brown Black Black Black Brown Blue Brown Black Black Black Brown Blue Brown Black Brown Blue Brown Brown Blue Brown
Row 5: Black Black Brown Blue Brown Brown Blue Brown Brown Blue Brown Black Brown Blue Brown Black Black Black Blue Black Blue Black Blue Black Blue Brown Blue Brown
Row 6: Black Black Blue Black Blue Blue Black Blue Blue Black Blue Black Blue Black Blue Brown Blue Brown Brown Blue Brown Black Brown Blue Brown Blue Black Blue
Row 7: Black Black Brown Blue Brown Brown Blue Brown Brown Blue Brown Black Brown Blue Brown Blue Black Blue Black Black Brown Blue Brown Black Black Brown Blue Brown
Row 8: Black Black Black Brown Blue Brown Black Black Black Black Black Black Black Black Black Brown Blue Brown Black Black Blue Black Blue Black Black Black Black Black
Row 9: Black Black Black Blue Black Blue Black Black Black Black Black Black Black Brown Blue Brown Brown Blue Brown Black Brown Blue Brown Brown Blue Brown Black Black
Row 10: Black Black Black Brown Blue Brown Black Black Brown Blue Brown Black Black Blue Black Blue Blue Black Blue Black Black Black Black Blue Black Blue Black Black
Row 11: Black Black Black Black Brown Blue Brown Black Blue Black Blue Black Black Brown Blue Brown Brown Blue Brown Brown Blue Brown Black Brown Blue Brown Black Black
Row 12: Brown Blue Brown Black Blue Black Blue Black Brown Blue Brown Black Black Black Black Black Black Black Black Blue Black Blue Black Black Black Black Black Black
Row 13: Blue Black Blue Black Brown Blue Brown Black Brown Blue Brown Black Black Black Black Black Black Black Black Brown Blue Brown Black Black Brown Blue Brown Black
Row 14: Brown Blue Brown Black Brown Blue Brown Black Blue Black Blue Brown Blue Brown Black Brown Blue Brown Black Brown Blue Brown Black Black Blue Black Blue Black
Row 15: Black Black Black Black Blue Black Blue Black Brown Blue Brown Blue Black Blue Black Blue Black Blue Black Blue Black Blue Black Black Brown Blue Brown Black
Row 16: Black Black Black Black Brown Blue Brown Black Black Black Black Brown Blue Brown Black Brown Blue Brown Black Brown Blue Brown Black Black Black Black Black Black
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Red Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Red Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Red Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Red Blue Red Black Black
Row 4: Black Black Black Black Black Black Black Black Blue Black Blue Black Black
Row 5: Black Black Black Black Black Black Black Black Red Blue Red Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Red Blue Red Black Black Black Black
Row 11: Black Black Black Black Black Black Blue Black Blue Black Black Black Black
Row 12: Black Black Black Black Black Black Red Blue Red Black Black Black Black
Row 13: Black Black Black Black Red Blue Red Black Black Black Black Black Black
Row 14: Black Black Black Black Blue Black Blue Black Black Black Black Black Black
Row 15: Black Black Black Black Red Blue Red Black Black Black Black Black Black
Example 3
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Purple Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Purple Blue Purple Orange Orange Orange
Row 4: Orange Orange Blue Orange Blue Orange Orange Orange
Row 5: Orange Orange Purple Blue Purple Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Brown Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Brown Red Red Red Brown Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Brown Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Brown Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Red
Row 14: Red Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Brown Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Brown Red Red Red Red Brown Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Red
Row 21: Red Brown Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 22: Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Red Red
Row 23: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red
Row 24: Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red
Row 25: Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 26: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 27: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red
Row 28: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Brown Blue Brown Red Red Red Red Brown Blue Brown Red Red Red Red Red Red Red Red Red Red Red Red Red
Blue Red Blue Red Red Red Red Blue Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red
Brown Blue Brown Red Red Red Red Brown Blue Brown Red Red Red Red Red Red Red Red Red Red Red Red Red
Brown Blue Brown Red Brown Blue Brown Red Red Brown Blue Brown Red Red Red Red Red Red Red Red Red Red Red
Blue Red Blue Red Blue Red Blue Red Red Blue Red Blue Red Red Red Red Red Red Red Brown Blue Brown Red
Brown Blue Brown Red Brown Blue Brown Red Red Brown Blue Brown Red Red Red Red Red Red Red Blue Red Blue Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Blue Brown Red
Red Red Red Red Red Red Red Red Red Red Red Brown Blue Brown Red Red Red Brown Blue Brown Red Red Red
Red Red Red Red Red Red Red Brown Blue Brown Red Blue Red Blue Red Red Red Blue Red Blue Red Red Red
Red Red Red Red Red Red Red Blue Red Blue Red Brown Blue Brown Red Red Red Brown Blue Brown Red Red Red
Red Red Red Red Brown Blue Brown Brown Blue Brown Red Brown Blue Brown Red Red Red Red Red Red Red Red Red
Brown Blue Brown Red Blue Red Blue Red Red Red Red Blue Red Blue Red Red Red Red Red Red Red Red Red
Blue Red Blue Red Brown Blue Brown Red Red Red Red Brown Blue Brown Brown Blue Brown Red Red Red Red Red Red
Brown Blue Brown Red Red Red Red Red Red Red Brown Blue Brown Red Blue Red Blue Red Brown Blue Brown Red Red
Red Red Red Red Red Red Red Red Red Red Blue Red Blue Red Brown Blue Brown Red Blue Red Blue Red Red
Brown Blue Brown Red Red Brown Blue Brown Red Red Brown Blue Brown Brown Blue Brown Red Red Brown Blue Brown Red Red
Blue Red Blue Red Red Blue Red Blue Red Red Brown Blue Brown Blue Red Blue Red Red Red Red Red Red Red
Brown Blue Brown Red Red Brown Blue Brown Red Red Blue Red Blue Brown Blue Brown Red Red Red Brown Blue Brown Red
Brown Blue Brown Red Red Red Red Brown Blue Brown Brown Blue Brown Red Red Red Red Red Red Blue Red Blue Red
Blue Red Blue Red Red Red Red Blue Red Blue Brown Blue Brown Red Red Red Red Red Red Brown Blue Brown Red
Brown Blue Brown Red Red Red Red Brown Blue Brown Blue Red Blue Brown Blue Brown Red Red Red Red Red Red Red
Red Red Red Red Brown Blue Brown Red Red Red Brown Blue Brown Blue Red Blue Brown Blue Brown Red Red Red Red
Red Red Red Red Blue Red Blue Red Brown Blue Brown Red Red Brown Blue Brown Blue Red Blue Red Red Red Red
Red Red Red Red Brown Blue Brown Red Blue Red Blue Red Red Red Red Red Brown Blue Brown Red Red Red Red
Red Red Red Red Red Red Red Red Brown Blue Brown Red Red Red Brown Blue Brown Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Blue Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Blue Brown Red Red Red Red Red Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Blue Orange Red Red Red Red Red
Row 2: Red Red Blue Blue Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Blue Orange Red Red
Row 5: Red Red Red Red Red Blue Blue Red Red
Row 6: Red Blue Orange Red Red Red Red Red Red
Row 7: Red Blue Blue Red Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Blue Blue Blue Blue Red Red Red Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Red Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 21: Red Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Example 2
Input:
Row 1: Yellow Yellow Yellow Green Blue Yellow Yellow Yellow Yellow
Row 2: Green Blue Yellow Green Green Yellow Yellow Yellow Yellow
Row 3: Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Green Blue Yellow Green Blue Yellow Yellow
Row 6: Yellow Yellow Green Green Yellow Green Green Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Blue Blue Purple Purple Purple
Row 3: Blue Blue Purple Blue Pink Purple Blue Blue
Row 4: Blue Pink Purple Purple Purple Purple Blue Pink
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Blue Blue Blue Blue Purple Purple Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Blue Blue Blue Blue Purple Purple Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Red Black
Row 4: Yellow Yellow Yellow Yellow Yellow Black Black
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Pink Black Red Pink
Row 2: Black Black Black Black Black
Row 3: Red Pink Black Pink Red
Output:
Row 1: Pink Red
Example 2
Input:
Row 1: Yellow Gray Blue Pink Yellow Gray Blue
Row 2: Red Purple Pink Pink Red Purple Pink
Row 3: Orange Pink Orange Pink Orange Pink Orange
Row 4: Pink Pink Brown Pink Pink Pink Brown
Row 5: Red Brown Pink Pink Red Brown Pink
Row 6: Pink Blue Pink Pink Pink Blue Pink
Row 7: Pink Pink Green Pink Pink Pink Green
Row 8: Pink Blue Pink Pink Pink Blue Pink
Row 9: Pink Gray Gray Pink Pink Gray Gray
Row 10: Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink
Row 12: Red Blue Red Pink Yellow Gray Blue
Row 13: Blue Brown Orange Pink Red Purple Pink
Row 14: Purple Purple Pink Pink Orange Pink Orange
Row 15: Gray Gray Yellow Pink Pink Pink Brown
Row 16: Brown Gray Yellow Pink Red Brown Pink
Row 17: Red Red Gray Pink Pink Blue Pink
Row 18: Pink Blue Orange Pink Pink Pink Green
Row 19: Orange Brown Orange Pink Pink Blue Pink
Row 20: Orange Red Brown Pink Pink Gray Gray
Row 21: Green Purple Blue Pink Pink Pink Pink
Output:
Row 1: Red Blue Red
Row 2: Blue Brown Orange
Row 3: Purple Purple Pink
Row 4: Gray Gray Yellow
Row 5: Brown Gray Yellow
Row 6: Red Red Gray
Row 7: Pink Blue Orange
Row 8: Orange Brown Orange
Row 9: Orange Red Brown
Row 10: Green Purple Blue
Example 3
Input:
Row 1: Purple Purple Gray Gray Purple Gray Purple Purple Yellow Gray Gray Purple Gray
Row 2: Purple Purple Gray Purple Gray Purple Purple Purple Yellow Gray Purple Gray Gray
Row 3: Purple Purple Gray Purple Gray Purple Purple Purple Purple Purple Purple Gray Gray
Row 4: Gray Purple Gray Gray Purple Gray Purple Gray Purple Gray Gray Purple Yellow
Row 5: Purple Gray Purple Purple Gray Yellow Purple Purple Gray Purple Yellow Gray Yellow
Row 6: Purple Gray Purple Gray Gray Gray Purple Purple Yellow Purple Gray Yellow Gray
Row 7: Gray Purple Purple Gray Purple Gray Purple Gray Purple Purple Gray Purple Yellow
Row 8: Yellow Purple Gray Purple Purple Gray Purple Yellow Yellow Gray Purple Gray Yellow
Row 9: Purple Purple Purple Purple Gray Purple Purple Yellow Gray Purple Purple Gray Purple
Row 10: Purple Gray Purple Yellow Purple Purple Purple Purple Yellow Purple Yellow Purple Purple
Row 11: Gray Purple Gray Gray Purple Gray Purple Purple Purple Gray Gray Purple Yellow
Row 12: Gray Purple Yellow Purple Gray Gray Purple Gray Purple Gray Yellow Yellow Gray
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Gray Gray Purple Gray Purple Purple Purple Gray Gray Purple Gray
Row 15: Purple Purple Gray Purple Gray Purple Purple Purple Purple Gray Purple Gray Purple
Row 16: Purple Purple Gray Purple Gray Purple Purple Purple Purple Gray Purple Gray Purple
Row 17: Gray Purple Gray Gray Purple Gray Purple Gray Purple Gray Gray Purple Gray
Row 18: Purple Gray Purple Purple Gray Yellow Purple Purple Gray Purple Purple Gray Yellow
Row 19: Purple Gray Purple Gray Gray Gray Purple Purple Gray Purple Gray Gray Gray
Row 20: Gray Purple Purple Gray Purple Gray Purple Gray Purple Purple Gray Purple Gray
Row 21: Yellow Purple Gray Purple Purple Gray Purple Yellow Purple Gray Purple Purple Gray
Row 22: Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Gray Purple
Row 23: Purple Gray Purple Yellow Purple Purple Purple Purple Gray Purple Yellow Purple Purple
Row 24: Gray Purple Gray Gray Purple Gray Purple Gray Purple Gray Gray Purple Gray
Row 25: Gray Purple Yellow Purple Gray Gray Purple Gray Purple Yellow Purple Gray Gray
Output:
Row 1: Purple Yellow Gray Gray Purple Gray
Row 2: Purple Yellow Gray Purple Gray Gray
Row 3: Purple Purple Purple Purple Gray Gray
Row 4: Gray Purple Gray Gray Purple Yellow
Row 5: Purple Gray Purple Yellow Gray Yellow
Row 6: Purple Yellow Purple Gray Yellow Gray
Row 7: Gray Purple Purple Gray Purple Yellow
Row 8: Yellow Yellow Gray Purple Gray Yellow
Row 9: Yellow Gray Purple Purple Gray Purple
Row 10: Purple Yellow Purple Yellow Purple Purple
Row 11: Purple Purple Gray Gray Purple Yellow
Row 12: Gray Purple Gray Yellow Yellow Gray
Here is the input grid for the test example:
Input:
Row 1: Blue Blue Gray
Row 2: Blue Blue Blue
Row 3: Green Blue Green
Row 4: Purple Blue Purple
Row 5: Gray Blue Gray
Row 6: Blue Blue Green
Row 7: Blue Blue Green
Row 8: Black Blue Gray
Row 9: Red Blue Gray
Row 10: Blue Blue Blue
Row 11: Blue Blue Blue
Row 12: Blue Blue Blue
Row 13: Green Blue Green
Row 14: Purple Blue Purple
Row 15: Gray Blue Gray
Row 16: Blue Blue Blue
Row 17: Blue Blue Blue
Row 18: Black Blue Black
Row 19: Red Blue Red
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray
Blue
Green
Purple
Gray
Green
Green
Gray
Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Black Black Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Black Black Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Black Pink
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Black Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Black Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Black Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Black Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Black Pink Black Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink
Row 17: Pink Pink Black Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Black Pink Black Pink Pink Pink Pink
Row 18: Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Green Green Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Green Pink
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Pink Pink Green Pink Pink Green Green Pink Pink Pink Pink Pink Pink Green Pink Green Pink Pink Pink Pink
Row 7: Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Green Pink Green Pink Pink Pink Pink
Row 8: Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Green Pink Green Pink Pink Pink Pink
Row 9: Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Green Pink Green Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Green Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Green Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Green Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Green Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Example 2
Input:
Row 1: Pink Brown Pink Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Pink Brown Pink Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Red Red Pink Brown Brown Brown Brown Brown Brown Pink Pink Brown Pink Brown Brown
Row 5: Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Pink Brown Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Red Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Red Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Red Red Red Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 3
Input:
Row 1: Green Green Orange Orange Green Black Black
Row 2: Green Green Orange Orange Black Green Green
Row 3: Green Green Orange Orange Green Black Green
Row 4: Green Green Orange Orange Green Green Green
Row 5: Green Green Orange Orange Green Green Black
Row 6: Green Green Orange Orange Green Green Green
Row 7: Green Green Orange Orange Black Green Green
Row 8: Black Green Orange Orange Green Green Green
Row 9: Green Green Orange Orange Green Green Green
Row 10: Black Green Orange Orange Black Green Black
Row 11: Green Black Orange Orange Green Green Green
Row 12: Green Green Orange Orange Green Green Green
Row 13: Green Green Orange Orange Green Green Green
Row 14: Green Green Orange Orange Green Green Green
Row 15: Green Green Orange Orange Green Green Green
Row 16: Green Green Orange Orange Green Green Green
Row 17: Green Green Orange Orange Green Green Black
Row 18: Green Green Orange Orange Green Green Green
Row 19: Green Green Orange Orange Green Black Green
Row 20: Green Green Orange Orange Green Green Green
Row 21: Green Green Orange Orange Black Green Black
Row 22: Green Black Orange Orange Green Black Black
Output:
Row 1: Green Green Orange Orange Orange Orange Green
Row 2: Green Green Orange Orange Orange Green Green
Row 3: Green Green Orange Orange Orange Green Green
Row 4: Green Green Orange Orange Green Green Green
Row 5: Green Green Orange Orange Orange Green Green
Row 6: Green Green Orange Orange Green Green Green
Row 7: Green Green Orange Orange Orange Green Green
Row 8: Green Orange Orange Orange Green Green Green
Row 9: Green Green Orange Orange Green Green Green
Row 10: Green Orange Orange Orange Orange Orange Green
Row 11: Green Orange Orange Orange Green Green Green
Row 12: Green Green Orange Orange Green Green Green
Row 13: Green Green Orange Orange Green Green Green
Row 14: Green Green Orange Orange Green Green Green
Row 15: Green Green Orange Orange Green Green Green
Row 16: Green Green Orange Orange Green Green Green
Row 17: Green Green Orange Orange Orange Green Green
Row 18: Green Green Orange Orange Green Green Green
Row 19: Green Green Orange Orange Orange Green Green
Row 20: Green Green Orange Orange Green Green Green
Row 21: Green Green Orange Orange Orange Orange Green
Row 22: Green Orange Orange Orange Orange Orange Green
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Row 10: Brown Yellow Brown Yellow Green Green Green Green Yellow Yellow
Row 11: Brown Yellow Brown Yellow Green Green Green Green Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Row 14: Yellow Brown Brown Brown Green Green Green Green Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Green Green Green Green Yellow Brown
Row 17: Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Green Green Green Green Brown Yellow
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Yellow Yellow Green Green Green Green Green Green Yellow Yellow
Yellow Yellow Green Green Green Green Green Green Yellow Yellow
Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Yellow Green Green Green Green Green Green Green Yellow Yellow
Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow
Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Yellow Yellow Yellow Yellow Green Green Green Green Yellow Yellow
Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Green Green Orange Pink Pink Orange Pink Pink Orange Pink Pink Orange Pink Pink Orange Pink Pink Orange Pink Pink Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Red Red Orange Pink Pink Orange Pink Pink Orange Pink Pink Orange Green Green Orange Pink Pink Orange Pink Pink Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Pink Pink Orange Pink Pink Orange Brown Brown Orange Pink Pink Orange Pink Pink Orange Pink Pink Orange Pink Pink Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Purple Purple Orange Pink Pink Orange Pink Pink Orange Pink Pink Orange Green Green Orange Pink Pink Orange Purple Purple Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Pink Pink Orange Purple Purple Orange Purple Purple Orange Yellow Yellow Orange Pink Pink Orange Pink Pink Orange Pink Pink Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Pink Pink Orange Pink Pink Orange Red Red Orange Pink Pink Orange Pink Pink Orange Pink Pink Orange Pink Pink Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Pink Pink Orange Pink Pink Orange Pink Pink Orange Pink Pink Orange Pink Pink Orange Purple Purple Orange Red Red Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Pink Pink Orange Yellow Yellow Orange Pink Pink Orange Red Red Orange Pink Pink Orange Pink Pink Orange Pink Pink Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Purple
Row 2: Red
Row 3: Green
Row 4: Yellow
Row 5: Brown
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink
Row 3: Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink
Row 4: Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink
Row 5: Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Brown Brown Brown Brown Brown Pink Orange Orange Orange Orange Orange Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink
Row 8: Pink Brown Brown Brown Brown Brown Pink Orange Orange Orange Orange Orange Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink
Row 9: Pink Brown Brown Brown Brown Brown Pink Orange Orange Orange Orange Orange Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink
Row 10: Pink Brown Brown Brown Brown Brown Pink Orange Orange Orange Orange Orange Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink
Row 13: Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink
Row 14: Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink
Row 15: Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink
Row 18: Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink
Row 19: Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink
Row 20: Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Orange
Example 3
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange
Row 3: Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange
Row 6: Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Pink Pink Pink Orange Black Black Black Orange Brown Brown Brown Orange Black Black Black Orange Black Black Black Orange
Row 9: Orange Pink Pink Pink Orange Black Black Black Orange Brown Brown Brown Orange Black Black Black Orange Black Black Black Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange
Row 12: Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Pink Pink Pink Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange
Row 15: Orange Pink Pink Pink Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Pink
Row 2: Brown
Here is the input grid for the test example:
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green
Row 3: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green
Row 6: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green
Row 9: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green
Row 12: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green
Row 15: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green
Row 16: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green
Row 18: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 20: Green Blue Blue Blue Blue Blue Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green
Row 21: Green Blue Blue Blue Blue Blue Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green
Row 24: Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green
Row 25: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 26: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 27: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Red Red Red
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 26: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 27: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 2
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray
Row 5: Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray
Row 6: Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray
Row 7: Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray
Row 8: Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray
Row 9: Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray
Row 10: Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray
Row 11: Orange Gray Gray Gray Gray Gray Orange Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray
Row 12: Orange Gray Gray Gray Gray Gray Orange Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray
Row 13: Orange Gray Gray Orange Gray Gray Orange Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray
Row 14: Orange Gray Gray Orange Gray Gray Orange Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray
Example 3
Input:
Row 1: Green Green Green Green Green Green Gray Green
Row 2: Green Gray Green Green Green Green Gray Green
Row 3: Green Gray Green Green Green Green Gray Green
Row 4: Green Gray Green Green Green Green Gray Green
Row 5: Green Gray Green Green Green Green Gray Green
Row 6: Green Gray Green Green Green Green Gray Green
Row 7: Green Gray Green Green Green Green Gray Green
Row 8: Green Gray Green Green Green Green Gray Green
Row 9: Green Gray Green Green Green Green Gray Green
Row 10: Green Gray Green Green Green Green Gray Green
Row 11: Green Gray Green Green Green Green Gray Green
Row 12: Green Gray Green Green Green Green Gray Green
Row 13: Green Gray Green Green Green Green Gray Green
Row 14: Green Gray Green Green Green Green Gray Green
Row 15: Green Gray Green Green Green Green Gray Green
Row 16: Green Gray Green Green Green Green Gray Green
Row 17: Green Gray Green Green Green Green Gray Green
Row 18: Green Gray Green Green Green Green Gray Green
Row 19: Green Gray Green Green Green Green Gray Green
Row 20: Green Gray Green Green Green Green Gray Green
Row 21: Green Gray Green Green Gray Green Gray Green
Row 22: Green Gray Green Green Gray Green Gray Green
Output:
Row 1: Green Green Green Green Green Green Blue Green
Row 2: Green Green Green Green Green Green Blue Green
Row 3: Green Green Green Green Green Green Blue Green
Row 4: Green Green Green Green Green Green Blue Green
Row 5: Green Green Green Green Green Green Blue Green
Row 6: Green Green Green Green Green Green Blue Green
Row 7: Green Green Green Green Green Green Blue Green
Row 8: Green Green Green Green Green Green Blue Green
Row 9: Green Green Green Green Green Green Blue Green
Row 10: Green Green Green Green Green Green Blue Green
Row 11: Green Green Green Green Green Green Blue Green
Row 12: Green Green Green Green Green Green Blue Green
Row 13: Green Green Green Green Green Green Blue Green
Row 14: Green Green Green Green Green Green Blue Green
Row 15: Green Green Green Green Green Green Blue Green
Row 16: Green Green Green Green Green Green Blue Green
Row 17: Green Green Green Green Green Green Blue Green
Row 18: Green Green Green Green Green Green Blue Green
Row 19: Green Green Green Green Green Green Blue Green
Row 20: Green Green Green Green Green Green Blue Green
Row 21: Green Green Green Green Red Green Blue Green
Row 22: Green Green Green Green Red Green Blue Green
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Orange Pink Orange
Row 2: Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Orange Pink Orange
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Orange
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Orange
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Orange
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Blue Pink Pink
Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Blue Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 2: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 3: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 4: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 5: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 6: Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Purple Brown Green Brown Brown Brown Brown Black Brown Brown Green Brown Brown
Row 7: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 8: Orange Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Brown Orange Pink Orange Purple Orange Green Orange Orange Orange Orange Black Orange Orange Green Orange Orange
Row 9: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 10: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 11: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 12: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 13: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 14: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 15: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 16: Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Pink Yellow Purple Yellow Green Yellow Yellow Yellow Yellow Black Yellow Yellow Green Yellow Yellow
Row 17: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 18: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 19: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 20: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 21: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 22: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 23: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 24: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 25: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 26: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 27: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Row 28: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Brown Gray Pink Gray Purple Gray Green Gray Gray Gray Gray Black Gray Gray Green Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray
Example 2
Input:
Row 1: Red Red Red Green Red Red Red Red Pink Red Red Red Red Yellow Red Red Red Red Red Yellow Red
Row 2: Red Red Red Green Red Red Red Red Pink Red Red Red Red Yellow Red Red Red Red Red Yellow Red
Row 3: Red Red Red Green Red Red Red Red Pink Red Red Red Red Yellow Red Red Red Red Red Yellow Red
Row 4: Red Red Red Green Red Red Red Red Pink Red Red Red Red Yellow Red Red Red Red Red Yellow Red
Row 5: Red Red Red Green Red Red Red Red Pink Red Red Red Red Yellow Red Red Red Red Red Yellow Red
Row 6: Red Red Red Green Red Red Red Red Pink Red Red Red Red Yellow Red Red Red Red Red Yellow Red
Row 7: Red Red Red Green Red Red Red Red Pink Red Red Red Red Yellow Red Red Red Red Red Yellow Red
Row 8: Purple Purple Purple Green Purple Purple Purple Purple Pink Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Yellow Purple
Row 9: Red Red Red Green Red Red Red Red Pink Red Red Red Red Yellow Red Red Red Red Red Yellow Red
Row 10: Red Red Red Green Red Red Red Red Pink Red Red Red Red Yellow Red Red Red Red Red Yellow Red
Output:
Row 1: Red Red Red Red Red
Row 2: Red Red Red Red Red
Example 3
Input:
Row 1: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 2: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 3: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 4: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 5: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 6: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 7: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 8: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 9: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 10: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 11: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 12: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 13: Red Red Red Green Red Red Pink Red Red Orange Red Blue Red Red Blue Red Blue Red Red Red Red Red Red
Row 14: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 15: Gray Gray Gray Green Gray Gray Pink Gray Gray Orange Gray Blue Gray Gray Blue Gray Blue Gray Gray Gray Gray Gray Gray
Row 16: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 17: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 18: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 19: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 20: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 21: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 22: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 23: Yellow Yellow Yellow Green Yellow Yellow Pink Yellow Yellow Orange Yellow Blue Yellow Yellow Blue Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Row 25: Black Black Black Green Black Black Pink Black Black Orange Black Blue Black Black Blue Black Blue Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Yellow Orange Orange Gray Orange Black Orange Purple Orange Orange Orange Orange Orange Purple Orange Pink Orange Orange Orange Orange Orange Orange Orange Green Orange
Row 2: Orange Orange Orange Yellow Orange Orange Gray Orange Black Orange Purple Orange Orange Orange Orange Orange Purple Orange Pink Orange Orange Orange Orange Orange Orange Orange Green Orange
Row 3: Orange Orange Orange Yellow Orange Orange Gray Orange Black Orange Purple Orange Orange Orange Orange Orange Purple Orange Pink Orange Orange Orange Orange Orange Orange Orange Green Orange
Row 4: Orange Orange Orange Yellow Orange Orange Gray Orange Black Orange Purple Orange Orange Orange Orange Orange Purple Orange Pink Orange Orange Orange Orange Orange Orange Orange Green Orange
Row 5: Orange Orange Orange Yellow Orange Orange Gray Orange Black Orange Purple Orange Orange Orange Orange Orange Purple Orange Pink Orange Orange Orange Orange Orange Orange Orange Green Orange
Row 6: Orange Orange Orange Yellow Orange Orange Gray Orange Black Orange Purple Orange Orange Orange Orange Orange Purple Orange Pink Orange Orange Orange Orange Orange Orange Orange Green Orange
Row 7: Orange Orange Orange Yellow Orange Orange Gray Orange Black Orange Purple Orange Orange Orange Orange Orange Purple Orange Pink Orange Orange Orange Orange Orange Orange Orange Green Orange
Row 8: Red Red Red Yellow Red Red Gray Red Black Red Purple Red Red Red Red Red Purple Red Pink Red Red Red Red Red Red Red Green Red
Row 9: Orange Orange Orange Yellow Orange Orange Gray Orange Black Orange Purple Orange Orange Orange Orange Orange Purple Orange Pink Orange Orange Orange Orange Orange Orange Orange Green Orange
Row 10: Orange Orange Orange Yellow Orange Orange Gray Orange Black Orange Purple Orange Orange Orange Orange Orange Purple Orange Pink Orange Orange Orange Orange Orange Orange Orange Green Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Purple Pink Purple Purple Purple Pink Pink Purple Pink Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Pink Pink Purple Purple Purple Purple Purple Purple Pink Purple
Row 3: Purple Purple Pink Purple Pink Purple Purple Pink Pink Purple Purple Purple Purple Purple
Row 4: Purple Pink Pink Purple Purple Purple Purple Pink Purple Pink Purple Purple Purple Pink
Row 5: Pink Purple Purple Purple Pink Purple Purple Purple Purple Pink Purple Purple Purple Purple
Row 6: Purple Purple Pink Purple Pink Purple Pink Pink Pink Purple Purple Pink Pink Purple
Row 7: Pink Purple Pink Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple
Row 8: Purple Purple Purple Pink Purple Purple Pink Pink Purple Purple Purple Purple Purple Purple
Row 9: Pink Purple Purple Pink Purple Pink Purple Purple Pink Purple Purple Purple Purple Purple
Row 10: Purple Pink Purple Purple Purple Pink Purple Purple Pink Pink Purple Pink Pink Pink
Row 11: Pink Purple Purple Pink Pink Purple Pink Pink Purple Purple Purple Purple Purple Purple
Row 12: Pink Pink Purple Pink Purple Pink Purple Purple Purple Pink Purple Purple Purple Purple
Output:
Row 1: Green Purple Green Purple Purple Purple Red Red Purple Green Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Blue Blue Purple Purple Purple Purple Purple Purple Green Purple
Row 3: Purple Purple Blue Purple Blue Purple Purple Blue Blue Purple Purple Purple Purple Purple
Row 4: Purple Blue Blue Purple Purple Purple Purple Blue Purple Red Purple Purple Purple Green
Row 5: Green Purple Purple Purple Red Purple Purple Purple Purple Red Purple Purple Purple Purple
Row 6: Purple Purple Red Purple Red Purple Blue Blue Blue Purple Purple Red Red Purple
Row 7: Green Purple Red Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple
Row 8: Purple Purple Purple Red Purple Purple Red Red Purple Purple Purple Purple Purple Purple
Row 9: Green Purple Purple Red Purple Red Purple Purple Blue Purple Purple Purple Purple Purple
Row 10: Purple Green Purple Purple Purple Red Purple Purple Blue Blue Purple Blue Blue Blue
Row 11: Blue Purple Purple Blue Blue Purple Red Red Purple Purple Purple Purple Purple Purple
Row 12: Blue Blue Purple Blue Purple Green Purple Purple Purple Green Purple Purple Purple Purple
Example 2
Input:
Row 1: Brown Brown Gray Brown Gray
Row 2: Brown Gray Gray Brown Gray
Row 3: Gray Brown Brown Gray Brown
Row 4: Brown Gray Brown Gray Gray
Row 5: Brown Gray Gray Gray Gray
Output:
Row 1: Blue Blue Gray Red Gray
Row 2: Blue Gray Gray Red Gray
Row 3: Gray Blue Blue Gray Green
Row 4: Red Gray Blue Gray Gray
Row 5: Red Gray Gray Gray Gray
Example 3
Input:
Row 1: Pink Pink Pink Yellow Pink Pink Pink
Row 2: Pink Pink Pink Yellow Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Yellow Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink
Row 13: Yellow Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Yellow Pink Pink Pink Pink
Row 16: Pink Pink Yellow Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Yellow Pink Pink Pink Pink Pink
Row 22: Pink Yellow Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Red Pink Pink Pink
Row 2: Pink Pink Pink Red Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Green Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink
Row 13: Green Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Red Pink Pink Pink Pink
Row 16: Pink Pink Red Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Red Pink Pink Pink Pink Pink
Row 22: Pink Red Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Orange Orange Purple Purple Orange Orange
Row 3: Orange Purple Orange Purple Orange Purple Purple
Row 4: Purple Purple Purple Purple Orange Purple Purple
Row 5: Orange Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Orange Purple Purple Purple
Row 7: Purple Purple Purple Orange Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Orange Orange Purple Purple Purple
Row 11: Orange Purple Purple Orange Purple Purple Purple
Row 12: Purple Purple Orange Purple Orange Orange Purple
Row 13: Orange Purple Purple Purple Orange Purple Purple
Row 14: Orange Orange Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Orange Orange Purple Purple Orange Orange
Row 18: Purple Purple Orange Purple Purple Orange Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Orange Purple Purple Purple Purple Purple
Row 21: Purple Orange Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Orange Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Orange Orange Purple Purple
Row 25: Purple Orange Purple Purple Orange Purple Purple
Row 26: Purple Purple Purple Orange Purple Purple Purple
Row 27: Purple Orange Orange Purple Purple Purple Purple
Row 28: Purple Purple Purple Orange Purple Orange Orange
Row 29: Purple Purple Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Purple
Purple Blue Blue Purple Purple Red Red
Green Purple Blue Purple Red Purple Purple
Purple Purple Purple Purple Red Purple Purple
Green Purple Purple Purple Purple Purple Purple
Purple Purple Purple Red Purple Purple Purple
Purple Purple Purple Red Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple
Purple Purple Blue Blue Purple Purple Purple
Green Purple Purple Blue Purple Purple Purple
Purple Purple Green Purple Blue Blue Purple
Blue Purple Purple Purple Blue Purple Purple
Blue Blue Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple
Purple Blue Blue Purple Purple Blue Blue
Purple Purple Blue Purple Purple Blue Purple
Purple Purple Purple Purple Purple Purple Purple
Purple Red Purple Purple Purple Purple Purple
Purple Red Purple Purple Purple Purple Purple
Purple Purple Purple Green Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Blue Blue Purple Purple
Purple Green Purple Purple Blue Purple Purple
Purple Purple Purple Green Purple Purple Purple
Purple Red Red Purple Purple Purple Purple
Purple Purple Purple Green Purple Red Red
Purple Purple Purple Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange Orange Orange Pink Orange Orange Pink Orange Orange Orange Orange Orange Pink Pink Orange Orange Orange Pink
Row 2: Pink Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange
Row 3: Pink Orange Pink Orange Pink Orange Orange Pink Orange Orange Orange Pink Orange Orange Pink Orange Pink Pink Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange
Row 5: Orange Orange Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink
Row 6: Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Pink Orange Pink Pink Orange Pink Pink Pink
Row 7: Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Pink Orange Pink Pink
Row 8: Pink Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange Pink Orange Orange Pink Pink Orange Orange Pink
Row 9: Orange Pink Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange
Row 11: Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Pink Orange Orange
Row 12: Pink Pink Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Pink Pink Pink
Row 13: Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Pink Pink Orange Pink Pink Pink Pink Orange
Row 14: Pink Orange Orange Pink Orange Pink Orange Orange Orange Orange Orange Orange Orange Pink Orange Pink Pink Orange Pink
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange Pink Pink Pink Pink Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange Pink Pink Pink Pink Pink
Row 22: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Orange Pink
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Pink Pink Pink Pink Pink Pink
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Orange Pink Pink Pink
Row 26: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Orange Pink Orange Pink
Row 27: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 28: Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Orange Pink Pink
Row 29: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange Pink Pink Pink Pink
Output:
Row 1: Orange Orange Orange Pink Pink Orange Orange Pink Pink
Row 2: Pink Orange Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Orange Pink Pink Pink Pink Pink Pink Pink Orange
Row 5: Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Orange Pink Pink Orange Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Orange Pink Pink Pink Pink Orange Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Orange Pink Pink Pink
Row 13: Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Orange Orange Pink Pink Orange Pink Pink Pink Pink
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Purple Orange Orange Orange
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Purple Orange Purple Orange Purple Orange Orange Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Purple Orange Orange Orange Purple Purple Orange Orange Purple Orange
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Purple Purple Orange Orange Purple Purple Orange Orange Purple Orange
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Purple Orange Purple Orange Orange Orange Orange Orange Orange Orange Purple
Row 7: Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Purple Orange Purple Purple Purple Orange Purple Orange
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Orange
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Purple Purple Orange Orange Orange Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Orange Purple
Row 12: Purple Orange Purple Purple Orange Orange Purple Purple Purple Purple Purple Orange Orange Orange Orange Purple Purple Purple Orange Purple Orange Orange Orange Purple Orange
Row 13: Orange Purple Purple Purple Purple Orange Purple Purple Orange Purple Purple Orange Orange Orange Purple Purple Orange Orange Orange Orange Purple Purple Purple Orange Orange
Row 14: Purple Purple Purple Orange Purple Orange Purple Purple Purple Orange Purple Orange Orange Orange Orange Orange Purple Orange Purple Purple Purple Purple Orange Purple Purple
Row 15: Orange Purple Orange Purple Purple Purple Orange Purple Orange Purple Orange Orange Orange Orange Orange Purple Orange Orange Orange Purple Purple Purple Orange Orange Orange
Row 16: Purple Purple Purple Orange Purple Orange Orange Orange Purple Purple Purple Orange Orange Orange Purple Orange Purple Orange Orange Purple Purple Orange Orange Purple Orange
Row 17: Purple Purple Orange Orange Purple Purple Orange Purple Purple Purple Purple Orange Orange Orange Purple Orange Purple Purple Orange Purple Orange Orange Purple Purple Orange
Row 18: Orange Purple Purple Purple Purple Orange Orange Orange Purple Purple Orange Orange Orange Orange Orange Purple Purple Orange Purple Purple Orange Orange Purple Purple Orange
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Orange Orange Orange Purple Purple Purple Purple Purple Orange Purple Purple Orange Orange Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Purple Purple Pink Pink Pink Purple Purple
Row 2: Pink Purple Pink Pink Pink Purple Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink
Row 4: Purple Purple Pink Pink Pink Purple Pink
Row 5: Pink Purple Pink Pink Pink Purple Pink
Row 6: Purple Pink Pink Pink Pink Purple Purple
Row 7: Pink Purple Pink Pink Pink Purple Purple
Row 8: Pink Pink Pink Pink Pink Purple Purple
Row 9: Purple Purple Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Purple Pink Pink Pink Purple Purple
Row 13: Purple Purple Pink Pink Pink Purple Pink
Row 14: Purple Pink Pink Pink Pink Purple Purple
Row 15: Pink Purple Pink Pink Pink Purple Purple
Row 16: Purple Pink Pink Pink Pink Purple Purple
Row 17: Purple Purple Pink Pink Pink Purple Purple
Row 18: Pink Pink Pink Pink Pink Purple Purple
Row 19: Pink Purple Pink Pink Pink Purple Pink
Output:
Row 1: Purple Purple Purple
Row 2: Pink Purple Pink
Row 3: Pink Purple Purple
Row 4: Purple Purple Pink
Row 5: Purple Purple Purple
Row 6: Purple Purple Purple
Row 7: Purple Purple Purple
Row 8: Purple Purple Purple
Row 9: Purple Purple Purple
Row 10: Pink Purple Pink
Here is the input grid for the test example:
Input:
Row 1: Yellow Black Yellow Black Black Black Black Yellow Black Black Yellow
Row 2: Black Black Black Black Black Black Black Yellow Yellow Black Yellow
Row 3: Black Black Yellow Yellow Black Black Black Yellow Yellow Black Yellow
Row 4: Black Yellow Yellow Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 5: Black Yellow Black Yellow Black Black Black Yellow Yellow Black Black
Row 6: Black Yellow Black Black Black Black Black Yellow Yellow Yellow Black
Row 7: Yellow Black Yellow Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Black Black Black Black Black Black Black Yellow Yellow
Row 9: Black Black Black Black Black Black Black Black Yellow Yellow Yellow
Row 10: Black Black Black Black Black Black Black Black Black Black Black
Row 11: Yellow Yellow Yellow Yellow Black Black Black Black Black Yellow Black
Row 12: Yellow Yellow Yellow Black Black Black Black Black Black Yellow Black
Row 13: Yellow Black Yellow Yellow Black Black Black Black Black Yellow Black
Row 14: Yellow Yellow Yellow Yellow Black Black Black Black Yellow Black Yellow
Row 15: Yellow Yellow Yellow Yellow Black Black Black Yellow Black Yellow Yellow
Row 16: Yellow Yellow Black Yellow Black Black Black Yellow Black Black Black
Row 17: Yellow Yellow Yellow Yellow Black Black Black Black Black Black Yellow
Row 18: Yellow Yellow Yellow Yellow Black Black Black Yellow Yellow Black Yellow
Row 19: Yellow Yellow Yellow Yellow Black Black Black Yellow Black Yellow Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Yellow Yellow Yellow Black Yellow
Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Pink Green Green Brown Pink Pink Pink Green Brown Orange Pink Orange Orange Brown Pink Orange Pink Pink
Row 2: Green Green Pink Pink Brown Pink Orange Pink Pink Brown Orange Orange Orange Orange Brown Orange Pink Pink Pink
Row 3: Green Green Green Pink Brown Pink Yellow Pink Pink Brown Orange Orange Orange Orange Brown Pink Pink Pink Orange
Row 4: Green Green Pink Green Brown Green Pink Green Pink Brown Orange Orange Pink Orange Brown Pink Pink Pink Pink
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Orange Pink Orange Orange Brown Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Orange Orange Brown Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Orange Orange Pink Brown Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Orange Orange Pink Orange Brown Pink Pink Pink Pink
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Orange Pink Pink Pink Brown Pink Pink Pink Pink Brown Orange Pink Pink Orange Brown Pink Orange Orange Pink
Row 12: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Orange Pink Pink Orange Brown Orange Orange Orange Pink
Row 13: Orange Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Orange Pink
Row 14: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Orange Pink Orange Pink Brown Pink Pink Orange Orange
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Pink Pink Green Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 17: Pink Green Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 18: Pink Green Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Pink Pink Pink Pink Brown Pink Pink Pink Green Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Brown Pink Orange Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Brown Pink Yellow Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Brown Green Pink Green Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink
Example 2
Input:
Row 1: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Blue Purple Pink Red Orange Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Blue Green Purple Pink Orange Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Red Pink Orange Red Orange Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Gray Red Red Yellow Orange Purple Purple Purple Purple
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Brown Purple Gray Purple Orange Purple Purple Purple Purple Orange Blue Purple Blue Pink Orange Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Blue Brown Pink Orange Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Blue Purple Purple Brown Orange Purple Purple Purple Purple
Row 19: Purple Blue Purple Purple Orange Purple Purple Purple Purple Orange Green Purple Brown Pink Orange Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Blue Purple Pink Red
Row 17: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Blue Green Purple Pink
Row 18: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Red Pink Purple Red
Row 19: Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Gray Red Red Yellow
Example 3
Input:
Row 1: Orange Orange Pink Brown Brown
Row 2: Orange Orange Pink Gray Purple
Row 3: Orange Orange Pink Gray Black
Row 4: Orange Orange Pink Orange Brown
Row 5: Orange Orange Pink Brown Brown
Row 6: Pink Pink Pink Pink Pink
Row 7: Brown Orange Pink Gray Orange
Row 8: Orange Orange Pink Orange Red
Row 9: Orange Black Pink Orange Gray
Row 10: Black Orange Pink Gray Purple
Row 11: Brown Black Pink Black Red
Row 12: Pink Pink Pink Pink Pink
Row 13: Orange Brown Pink Brown Yellow
Row 14: Brown Brown Pink Black Orange
Row 15: Gray Orange Pink Green Brown
Row 16: Green Green Pink Red Purple
Row 17: Orange Orange Pink Black Gray
Row 18: Pink Pink Pink Pink Pink
Row 19: Orange Orange Pink Orange Orange
Row 20: Orange Orange Pink Orange Orange
Row 21: Orange Orange Pink Green Brown
Row 22: Orange Orange Pink Orange Orange
Row 23: Orange Orange Pink Orange Orange
Row 24: Pink Pink Pink Pink Pink
Row 25: Orange Orange Pink Orange Orange
Row 26: Orange Orange Pink Orange Orange
Row 27: Orange Orange Pink Orange Orange
Row 28: Orange Orange Pink Orange Orange
Row 29: Orange Orange Pink Orange Orange
Output:
Row 1: Orange Orange Pink Brown Yellow
Row 2: Orange Orange Pink Black Orange
Row 3: Orange Orange Pink Green Brown
Row 4: Orange Orange Pink Red Purple
Row 5: Orange Orange Pink Black Gray
Row 6: Pink Pink Pink Pink Pink
Row 7: Orange Orange Pink Orange Orange
Row 8: Orange Orange Pink Orange Orange
Row 9: Orange Orange Pink Orange Orange
Row 10: Orange Orange Pink Orange Orange
Row 11: Orange Orange Pink Orange Orange
Row 12: Pink Pink Pink Pink Pink
Row 13: Orange Orange Pink Orange Orange
Row 14: Orange Orange Pink Orange Orange
Row 15: Orange Orange Pink Orange Orange
Row 16: Orange Orange Pink Orange Orange
Row 17: Orange Orange Pink Orange Orange
Row 18: Pink Pink Pink Pink Pink
Row 19: Orange Orange Pink Orange Orange
Row 20: Orange Orange Pink Orange Orange
Row 21: Orange Orange Pink Orange Orange
Row 22: Orange Orange Pink Orange Orange
Row 23: Orange Orange Pink Orange Orange
Row 24: Pink Pink Pink Pink Pink
Row 25: Orange Orange Pink Orange Orange
Row 26: Orange Orange Pink Orange Orange
Row 27: Orange Orange Pink Orange Orange
Row 28: Orange Orange Pink Orange Orange
Row 29: Orange Orange Pink Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Gray Orange Pink Pink Gray Black Pink Pink
Row 2: Pink Pink Pink Gray Pink Pink Pink Gray Red Pink Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Red Purple Yellow Gray Pink Pink Pink Gray Pink Pink Pink
Row 5: Gray Pink Orange Gray Pink Pink Pink Gray Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Pink Gray Pink Pink Pink Gray Red Purple Yellow
Pink Pink Pink Gray Pink Pink Pink Gray Pink Pink Orange
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Pink Pink Pink Gray Pink Pink Pink Gray Pink Pink Pink
Pink Pink Pink Gray Pink Pink Pink Gray Pink Pink Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Yellow Blue Red Purple Black
Row 2: Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Pink Black Yellow Red Blue
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Orange Black Red Pink Pink
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown
Row 5: Brown Brown Yellow Brown Brown Brown Brown Yellow Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown
Output:
Row 1: Yellow Blue Red Purple Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Yellow Blue Red Purple Black
Row 2: Pink Black Yellow Red Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Pink Black Yellow Red Blue
Row 3: Orange Black Red Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Orange Black Red Pink Pink
Row 4: Yellow Blue Red Purple Black Yellow Blue Red Purple Black Yellow Blue Red Purple Black Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown
Row 5: Pink Black Yellow Red Blue Pink Black Yellow Red Blue Pink Black Yellow Red Blue Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown
Row 6: Orange Black Red Pink Pink Orange Black Red Pink Pink Orange Black Red Pink Pink Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown
Example 2
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink Pink Gray Pink Yellow
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Yellow Pink Pink Yellow Pink
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Gray Pink Gray Yellow Pink
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink Yellow Blue Pink Gray
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink Yellow Pink Gray Yellow
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink Blue Yellow Gray Yellow
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Gray Gray Gray Blue Gray
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Blue Red Red Red Red Blue Red Red Orange Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 21: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 22: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 23: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 24: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 25: Red Red Red Red Red Red Red Blue Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 26: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 27: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 28: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink Pink Gray Pink Yellow
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Yellow Pink Pink Yellow Pink
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Gray Pink Gray Yellow Pink
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink Yellow Blue Pink Gray
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink Yellow Pink Gray Yellow
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink Blue Yellow Gray Yellow
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Gray Gray Gray Blue Gray
Row 8: Red Red Red Red Red Pink Pink Gray Pink Yellow Pink Pink Gray Pink Yellow Orange Red Red Red Red Red
Row 9: Red Red Red Red Red Yellow Pink Pink Yellow Pink Yellow Pink Pink Yellow Pink Orange Red Red Red Red Red
Row 10: Red Red Red Red Red Gray Pink Gray Yellow Pink Gray Pink Gray Yellow Pink Orange Red Red Red Red Red
Row 11: Red Red Red Red Red Pink Yellow Blue Pink Gray Pink Yellow Blue Pink Gray Orange Red Red Red Red Red
Row 12: Red Red Red Red Red Pink Yellow Pink Gray Yellow Pink Yellow Pink Gray Yellow Orange Red Red Red Red Red
Row 13: Red Red Red Red Red Pink Blue Yellow Gray Yellow Pink Blue Yellow Gray Yellow Orange Red Red Red Red Red
Row 14: Red Red Red Red Red Gray Gray Gray Blue Gray Gray Gray Gray Blue Gray Orange Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 21: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 22: Red Red Red Red Red Pink Pink Gray Pink Yellow Red Red Red Red Red Orange Red Red Red Red Red
Row 23: Red Red Red Red Red Yellow Pink Pink Yellow Pink Red Red Red Red Red Orange Red Red Red Red Red
Row 24: Red Red Red Red Red Gray Pink Gray Yellow Pink Red Red Red Red Red Orange Red Red Red Red Red
Row 25: Red Red Red Red Red Pink Yellow Blue Pink Gray Red Red Red Red Red Orange Red Red Red Red Red
Row 26: Red Red Red Red Red Pink Yellow Pink Gray Yellow Red Red Red Red Red Orange Red Red Red Red Red
Row 27: Red Red Red Red Red Pink Blue Yellow Gray Yellow Red Red Red Red Red Orange Red Red Red Red Red
Row 28: Red Red Red Red Red Gray Gray Gray Blue Gray Red Red Red Red Red Orange Red Red Red Red Red
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Black Black Green Orange
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Gray Purple Blue Green
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Black Green Green Purple
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Orange Gray Blue Orange
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Purple Gray Purple Green
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Black Black Green Orange
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Gray Purple Blue Green
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Black Green Green Purple
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Orange Gray Blue Orange
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Purple Gray Purple Green
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Blue Black Black Green Orange Blue Black Black Green Orange Pink Pink Pink Pink Pink Blue Black Black Green Orange
Row 8: Purple Gray Purple Blue Green Purple Gray Purple Blue Green Pink Pink Pink Pink Pink Purple Gray Purple Blue Green
Row 9: Orange Black Green Green Purple Orange Black Green Green Purple Pink Pink Pink Pink Pink Orange Black Green Green Purple
Row 10: Purple Orange Gray Blue Orange Purple Orange Gray Blue Orange Pink Pink Pink Pink Pink Purple Orange Gray Blue Orange
Row 11: Green Purple Gray Purple Green Green Purple Gray Purple Green Pink Pink Pink Pink Pink Green Purple Gray Purple Green
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Orange Pink Pink Orange Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Orange Orange Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Pink Pink Orange Orange Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Pink Pink Pink Pink Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Brown Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Pink Pink Orange Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Orange Orange Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Pink Pink Orange Orange Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Pink Pink Pink Pink Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Orange Pink Pink Orange Pink Yellow Yellow Yellow Yellow Yellow Orange Pink Pink Orange Pink
Orange Orange Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Orange Orange Pink Pink Pink
Pink Pink Orange Orange Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Orange Orange Pink
Pink Pink Pink Pink Orange Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Orange
Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Pink Pink Orange Pink
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Pink Pink Pink
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Orange Orange Pink
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Orange
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Orange Pink Pink Orange Pink Orange Pink Pink Orange Pink
Yellow Yellow Yellow Yellow Yellow Orange Orange Pink Pink Pink Orange Orange Pink Pink Pink
Yellow Yellow Yellow Yellow Yellow Pink Pink Orange Orange Pink Pink Pink Orange Orange Pink
Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Orange Pink Pink Pink Pink Orange
Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Green Green Gray Gray Gray Gray Gray
Row 2: Green Green Green Green Gray Gray Gray Gray
Row 3: Green Green Green Green Green Gray Gray Gray
Row 4: Green Green Green Green Green Gray Gray Gray
Row 5: Green Green Green Gray Gray Gray Gray Gray
Row 6: Green Green Green Green Gray Gray Gray Gray
Row 7: Green Green Green Green Gray Gray Gray Gray
Row 8: Green Green Green Green Green Gray Gray Gray
Output:
Row 1: Green Gray
Example 2
Input:
Row 1: Black Black Black Black Brown Brown Brown Green Green Green Purple Purple Purple Purple Pink Pink Pink Pink Red Red Gray Gray Gray Gray Yellow Yellow Yellow
Row 2: Black Black Black Black Black Brown Brown Brown Green Green Green Green Purple Pink Pink Pink Pink Red Red Red Gray Gray Gray Gray Yellow Yellow Yellow
Row 3: Black Black Black Black Black Brown Brown Green Green Green Purple Purple Purple Purple Pink Pink Pink Red Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow
Row 4: Black Black Black Black Black Brown Green Green Green Green Purple Purple Purple Purple Pink Pink Pink Red Red Red Gray Gray Gray Gray Gray Yellow Yellow
Row 5: Black Black Black Black Brown Green Green Green Green Green Purple Purple Purple Purple Purple Pink Red Red Red Red Gray Gray Gray Gray Gray Gray Yellow
Row 6: Black Black Black Brown Brown Brown Green Green Green Green Purple Purple Purple Purple Pink Pink Pink Pink Red Gray Gray Gray Yellow Yellow Yellow Yellow Yellow
Row 7: Black Black Black Black Black Black Brown Green Green Green Purple Purple Purple Purple Purple Pink Red Red Red Red Red Gray Yellow Yellow Yellow Yellow Yellow
Row 8: Black Black Black Black Brown Brown Green Green Green Green Purple Purple Purple Purple Pink Red Red Red Red Red Gray Gray Gray Gray Yellow Yellow Yellow
Row 9: Black Black Black Brown Brown Brown Green Green Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Red Red Gray Gray Gray Yellow Yellow Yellow Yellow
Row 10: Black Black Black Black Brown Brown Brown Green Green Green Purple Purple Purple Pink Pink Pink Red Red Red Red Red Gray Gray Gray Yellow Yellow Yellow
Output:
Row 1: Black Brown Green Purple Pink Red Gray Yellow
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown
Row 3: Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Brown Black Black Brown Brown Brown Black
Row 4: Black Brown Brown Black Black Black Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 5: Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Green Black Green Black Black Green Green Green Green Black Black
Row 7: Green Black Green Green Black Green Green Green Green Green Black Green Green Green Green Black Black
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Red Green Green Green Green
Row 12: Green Red Green Red Red Green Green Green Red Green Red Green Red Green Red Green Red
Row 13: Red Red Red Red Red Green Green Red Red Red Red Red Red Green Red Red Red
Row 14: Purple Red Red Red Red Red Green Red Red Red Red Red Red Green Red Red Red
Row 15: Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Purple Red Purple Red Red Red Purple Red Purple Red Red Red Red Red Purple Purple Red
Row 17: Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Red
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Brown
Row 2: Black
Row 3: Green
Row 4: Red
Row 5: Purple
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Green Green Red Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Black Black Blue Black Black Black Black Blue Black Black Black Black Black Black Blue
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Pink Black Black Black Black Black Black Black Black Black
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 27: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 28: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 29: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown
Red
Green
Purple
Blue
Black
Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Green Brown Gray Brown Gray
Row 2: Brown Red Brown Red Brown Brown Brown Brown Brown Brown Gray
Row 3: Green Brown Red Gray Brown Brown Brown Brown Brown Gray Red
Row 4: Brown Brown Brown Brown Brown Brown Gray Brown Brown Gray Brown
Row 5: Brown Brown Brown Brown Red Green Gray Brown Gray Gray Brown
Row 6: Brown Red Brown Brown Brown Red Brown Green Brown Brown Gray
Row 7: Gray Brown Brown Brown Brown Brown Red Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green
Row 9: Red Brown Brown Brown Green Brown Red Brown Green Gray Brown
Row 10: Brown Brown Gray Brown Brown Brown Brown Brown Red Brown Brown
Row 11: Green Brown Gray Brown Brown Gray Green Brown Red Green Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Green Brown Gray Brown Gray
Row 2: Brown Red Brown Red Brown Brown Brown Brown Brown Brown Gray
Row 3: Green Brown Red Gray Brown Brown Brown Brown Brown Gray Red
Row 4: Brown Brown Brown Brown Brown Brown Gray Brown Brown Gray Brown
Row 5: Brown Brown Brown Brown Brown Purple Gray Brown Gray Gray Brown
Row 6: Brown Red Brown Brown Brown Brown Brown Green Brown Brown Gray
Row 7: Gray Brown Brown Brown Brown Brown Red Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green
Row 9: Red Brown Brown Brown Green Brown Red Brown Purple Gray Brown
Row 10: Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Green Brown Gray Brown Brown Gray Green Brown Brown Purple Brown
Example 2
Input:
Row 1: Yellow Yellow Yellow Yellow Red Yellow
Row 2: Yellow Green Yellow Green Green Yellow
Row 3: Green Red Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Brown
Row 5: Yellow Green Brown Yellow Yellow Yellow
Row 6: Yellow Red Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Purple Yellow Green Purple Yellow
Row 3: Purple Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Brown
Row 5: Yellow Purple Brown Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow
Example 3
Input:
Row 1: Red Pink Red Blue Pink
Row 2: Pink Blue Pink Blue Blue
Row 3: Red Blue Green Blue Blue
Row 4: Red Blue Blue Blue Pink
Row 5: Blue Blue Blue Blue Red
Row 6: Blue Blue Blue Blue Green
Row 7: Blue Blue Blue Blue Blue
Row 8: Green Green Blue Blue Blue
Row 9: Green Blue Blue Blue Pink
Row 10: Blue Blue Blue Pink Blue
Row 11: Green Blue Blue Blue Blue
Row 12: Blue Red Blue Blue Blue
Row 13: Blue Blue Blue Blue Pink
Row 14: Blue Red Blue Green Blue
Output:
Row 1: Red Pink Red Blue Pink
Row 2: Pink Blue Pink Blue Blue
Row 3: Red Blue Green Blue Blue
Row 4: Red Blue Blue Blue Pink
Row 5: Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Purple
Row 7: Blue Blue Blue Blue Blue
Row 8: Green Green Blue Blue Blue
Row 9: Green Blue Blue Blue Pink
Row 10: Blue Blue Blue Pink Blue
Row 11: Green Blue Blue Blue Blue
Row 12: Blue Red Blue Blue Blue
Row 13: Blue Blue Blue Blue Pink
Row 14: Blue Red Blue Green Blue
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Green Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Red Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 24: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray
Row 25: Gray Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray
Row 26: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Gray Gray
Row 27: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Green Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue
Row 2: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Blue Blue Blue Black Blue Blue Blue Black Blue Gray Orange Black Blue Blue Blue Black Blue Gray Orange
Row 5: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Yellow Blue Black Blue Blue Blue
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue
Row 8: Blue Blue Blue Black Blue Blue Blue Black Blue Brown Blue Black Blue Blue Blue Black Blue Blue Blue
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Blue Blue Blue Black Pink Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Pink Blue Blue
Row 11: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Yellow Blue Black Blue Blue Blue
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue
Row 14: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue
Row 17: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Blue Blue Blue Black Blue Blue Blue Black Blue Gray Blue Black Blue Blue Blue Black Blue Blue Blue
Row 20: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Orange
Row 23: Blue Brown Blue Black Blue Blue Blue Black Blue Brown Blue Black Blue Blue Blue Black Blue Blue Blue
Row 24: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 25: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue
Row 26: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Yellow Blue Black Blue Blue Blue
Row 27: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 28: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue
Row 29: Blue Blue Blue Black Blue Blue Blue Black Blue Brown Blue Black Blue Blue Blue Black Blue Blue Blue
Output:
Row 1: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue
Row 2: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Blue Blue Blue Black Blue Blue Blue Black Blue Gray Orange Black Blue Gray Orange Black Blue Gray Orange
Row 5: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Yellow Blue Black Blue Blue Blue
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Blue Blue Blue Black Blue Blue Blue Black Blue Gray Blue Black Blue Blue Blue Black Blue Blue Orange
Row 8: Blue Blue Blue Black Blue Blue Blue Black Blue Brown Blue Black Blue Yellow Blue Black Blue Blue Blue
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Blue Blue Blue Black Pink Blue Blue Black Pink Gray Blue Black Pink Blue Blue Black Pink Blue Orange
Row 11: Blue Blue Blue Black Blue Blue Blue Black Blue Brown Blue Black Blue Yellow Blue Black Blue Blue Blue
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Blue Blue Blue Black Blue Blue Blue Black Blue Gray Blue Black Blue Blue Blue Black Blue Blue Orange
Row 14: Blue Blue Blue Black Blue Blue Blue Black Blue Brown Blue Black Blue Yellow Blue Black Blue Blue Blue
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Blue Blue Blue Black Blue Blue Blue Black Blue Gray Blue Black Blue Blue Blue Black Blue Blue Orange
Row 17: Blue Blue Blue Black Blue Blue Blue Black Blue Brown Blue Black Blue Yellow Blue Black Blue Blue Blue
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Blue Blue Blue Black Blue Blue Blue Black Blue Gray Blue Black Blue Blue Blue Black Blue Blue Orange
Row 20: Blue Blue Blue Black Blue Blue Blue Black Blue Brown Blue Black Blue Yellow Blue Black Blue Blue Blue
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Orange
Row 23: Blue Brown Blue Black Blue Brown Blue Black Blue Brown Blue Black Blue Yellow Blue Black Blue Blue Blue
Row 24: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 25: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue
Row 26: Blue Blue Blue Black Blue Blue Blue Black Blue Brown Blue Black Blue Yellow Blue Black Blue Blue Blue
Row 27: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 28: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue
Row 29: Blue Blue Blue Black Blue Blue Blue Black Blue Brown Blue Black Blue Blue Blue Black Blue Blue Blue
Example 2
Input:
Row 1: Red Black Red Black Red Black Red Black Red Black Yellow Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Yellow
Row 2: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red
Row 3: Purple Black Red Black Purple Black Red Black Red Black Red Black Red Black Purple Black Red Black Red Black Red Black Green Black Red Black Green
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Gray Black Red Black Red Black Gray Black Red Black Red Black Red
Row 6: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Blue Black Red Black Red Black Red Black Red Black Orange Black Red
Row 7: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Pink Black Red Black Red Black Red Black Red
Row 10: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red
Row 11: Red Black Red Black Purple Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Gray Black Red Black Red Black Red Black Red Black Red Black Yellow
Row 14: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Orange Black Red
Row 15: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Pink Black Red Black Red Black Red Black Red
Row 18: Red Black Red Black Blue Black Red Black Red Black Red Black Red Black Blue Black Red Black Blue Black Red Black Red Black Red Black Red
Row 19: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Green Black Red Black Red
Output:
Row 1: Red Black Red Black Red Black Red Black Red Black Yellow Black Yellow Black Yellow Black Yellow Black Yellow Black Yellow Black Yellow Black Yellow Black Yellow
Row 2: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red
Row 3: Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Red Black Red Black Red Black Green Black Green Black Green
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Gray Black Gray Black Gray Black Gray Black Red Black Red Black Yellow
Row 6: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Blue Black Red Black Red Black Red Black Red Black Orange Black Red
Row 7: Red Black Red Black Purple Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Green Black Red Black Red
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Gray Black Red Black Pink Black Red Black Red Black Red Black Yellow
Row 10: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Blue Black Red Black Red Black Red Black Red Black Orange Black Red
Row 11: Red Black Red Black Purple Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Green Black Red Black Red
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Gray Black Red Black Pink Black Red Black Red Black Red Black Yellow
Row 14: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Blue Black Red Black Red Black Red Black Red Black Orange Black Red
Row 15: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Green Black Red Black Red
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Pink Black Red Black Red Black Red Black Red
Row 18: Red Black Red Black Blue Black Blue Black Blue Black Blue Black Blue Black Blue Black Blue Black Blue Black Red Black Red Black Red Black Red
Row 19: Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Green Black Red Black Red
Example 3
Input:
Row 1: Purple Purple Purple Gray Purple Purple Red Gray Purple Purple Purple Gray Purple Purple Purple
Row 2: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple
Row 3: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Orange Purple Purple Gray Purple Purple Purple Gray Orange Purple Purple Gray Purple Purple Purple
Row 6: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple
Row 7: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Brown Purple
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Purple Purple Purple Gray Purple Purple Red Gray Purple Purple Purple Gray Purple Purple Purple
Row 10: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple
Row 11: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Orange Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple
Row 14: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple
Row 15: Purple Purple Purple Gray Purple Brown Purple Gray Purple Purple Purple Gray Purple Brown Purple
Output:
Row 1: Purple Purple Purple Gray Purple Purple Red Gray Purple Purple Purple Gray Purple Purple Purple
Row 2: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple
Row 3: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Orange Purple Purple Gray Orange Purple Red Gray Orange Purple Purple Gray Purple Purple Purple
Row 6: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple
Row 7: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Brown Purple
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Orange Purple Purple Gray Purple Purple Red Gray Purple Purple Purple Gray Purple Purple Purple
Row 10: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple
Row 11: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Brown Purple
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Orange Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple
Row 14: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple
Row 15: Purple Purple Purple Gray Purple Brown Purple Gray Purple Brown Purple Gray Purple Brown Purple
Here is the input grid for the test example:
Input:
Row 1: Green Green Red Green Green Red Green Gray Red Green Green Red Green Green Red Green Green Red Green Green Red Green Green
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Green Green Red Green Green Red Green Green Red Green Green Red Green Green Red Black Green Red Green Green Red Green Green
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Green Green Red Green Green Red Green Green Red Green Green Red Green Green Red Green Green Red Green Green Red Green Green
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Green Green Red Green Green Red Green Green Red Green Green Red Green Green Red Green Green Red Green Green Red Green Green
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Green Green Red Green Green Red Green Green Red Green Green Red Green Green Red Green Pink Red Green Green Red Green Green
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Purple Green Red Green Green Red Purple Green Red Green Green Red Purple Green Red Green Green Red Green Green Red Green Green
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Green Green Red Green Green Red Green Green Red Green Pink Red Green Green Red Green Pink Red Green Green Red Green Pink
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Green Green Red Green Green Red Green Green Red Green Green Red Green Green Red Green Green Red Brown Green Red Green Green
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Green Gray Red Green Green Red Green Gray Red Green Green Red Green Green Red Black Green Red Green Gray Red Green Green
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Green Green Red Green Green Red Purple Green Red Green Green Red Brown Green Red Green Green Red Brown Green Red Green Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Green Red Green Green Red Green Gray Red Green Green Red Green Green Red Green Green Red Green Green Red Green Green
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Green Green Red Green Green Red Green Gray Red Green Green Red Green Green Red Black Green Red Green Green Red Green Green
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Green Green Red Green Green Red Green Gray Red Green Green Red Green Green Red Black Green Red Green Green Red Green Green
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Green Green Red Green Green Red Green Gray Red Green Green Red Green Green Red Black Green Red Green Green Red Green Green
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Green Green Red Green Green Red Green Gray Red Green Green Red Green Green Red Black Pink Red Green Green Red Green Green
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Purple Green Red Purple Green Red Purple Gray Red Purple Green Red Purple Green Red Black Pink Red Green Green Red Green Green
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Green Green Red Green Green Red Purple Gray Red Green Pink Red Green Pink Red Black Pink Red Green Pink Red Green Pink
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Green Green Red Green Green Red Purple Gray Red Green Green Red Green Green Red Black Green Red Brown Green Red Green Green
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Green Gray Red Green Gray Red Purple Gray Red Green Gray Red Green Gray Red Black Gray Red Brown Gray Red Green Green
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Green Green Red Green Green Red Purple Green Red Green Green Red Brown Green Red Brown Green Red Brown Green Red Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Gray Blue Blue Blue Gray Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Gray
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Gray Blue Blue Blue Blue Blue
Row 3: Blue Gray Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Gray Blue Blue Blue Blue Gray Blue Blue Blue Gray Blue Blue Blue Blue Gray Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Gray
Row 7: Blue Gray Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Gray Blue Blue Gray Blue Blue
Row 8: Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue
Row 9: Gray Blue Blue Blue Blue Blue Gray Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Gray
Row 10: Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue
Row 11: Blue Gray Blue Blue Blue Gray Blue Blue Gray Blue Blue Gray Blue Blue Gray Blue Blue Blue Blue
Output:
Row 1: Gray Pink Blue Orange Gray Pink Orange Gray Pink Blue Red Blue Blue Red Orange Gray Pink Orange Gray
Row 2: Purple Red Blue Blue Purple Blue Red Purple Blue Orange Gray Pink Orange Gray Pink Purple Blue Blue Purple
Row 3: Orange Gray Pink Red Blue Orange Gray Pink Red Blue Purple Blue Red Purple Blue Blue Blue Red Blue
Row 4: Blue Purple Orange Gray Pink Blue Purple Orange Gray Pink Blue Orange Gray Pink Red Blue Orange Gray Pink
Row 5: Blue Blue Blue Purple Blue Red Blue Blue Purple Blue Red Blue Purple Orange Gray Pink Blue Purple Red
Row 6: Blue Red Blue Blue Orange Gray Pink Red Blue Orange Gray Pink Blue Red Purple Blue Red Orange Gray
Row 7: Orange Gray Pink Blue Red Purple Orange Gray Pink Blue Purple Red Orange Gray Pink Orange Gray Pink Purple
Row 8: Red Purple Blue Orange Gray Pink Red Purple Blue Red Orange Gray Pink Purple Blue Blue Purple Blue Red
Row 9: Gray Pink Blue Red Purple Orange Gray Pink Orange Gray Pink Purple Blue Blue Blue Blue Red Orange Gray
Row 10: Purple Red Orange Gray Pink Red Purple Blue Red Purple Blue Red Blue Blue Red Orange Gray Pink Purple
Row 11: Orange Gray Pink Purple Orange Gray Pink Orange Gray Pink Orange Gray Pink Orange Gray Pink Purple Blue Blue
Example 2
Input:
Row 1: Black Black Black Black Green Black Black Green Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Green Black Black Black Green Black Black Black Black Black
Row 4: Black Black Black Green Black Black Black Black Black Black Green
Row 5: Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Green Black Black Black Black
Row 7: Green Black Black Black Black Black Black Black Black Green Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Orange Green Pink Orange Green Pink Black Black
Row 2: Black Red Black Black Purple Red Black Purple Black Black Black
Row 3: Orange Green Pink Red Orange Green Pink Black Black Black Red
Row 4: Black Purple Orange Green Pink Purple Black Black Black Orange Green
Row 5: Black Black Black Purple Black Black Red Black Black Black Purple
Row 6: Red Black Black Black Black Orange Green Pink Black Red Black
Row 7: Green Pink Black Black Black Black Purple Black Orange Green Pink
Row 8: Purple Black Black Black Black Black Black Black Black Purple Black
Example 3
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Yellow Gray Gray Gray
Row 5: Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Yellow
Row 9: Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Yellow Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray
Row 12: Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Yellow Gray Gray Yellow
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray
Row 18: Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray
Row 21: Gray Gray Gray Gray Yellow Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Red Gray Gray Gray Gray Orange Yellow Pink Gray Gray Red
Row 3: Gray Gray Gray Orange Yellow Pink Gray Gray Red Gray Purple Red Gray Orange Yellow
Row 4: Gray Red Gray Gray Purple Gray Gray Orange Yellow Pink Orange Yellow Pink Gray Purple
Row 5: Orange Yellow Pink Gray Gray Gray Gray Gray Purple Red Gray Purple Gray Gray Gray
Row 6: Gray Purple Gray Red Gray Gray Gray Gray Orange Yellow Pink Gray Gray Gray Gray
Row 7: Gray Gray Orange Yellow Pink Red Gray Gray Gray Purple Gray Gray Gray Gray Red
Row 8: Gray Gray Red Purple Orange Yellow Pink Gray Gray Gray Gray Gray Gray Orange Yellow
Row 9: Gray Orange Yellow Pink Red Purple Gray Gray Gray Red Gray Gray Gray Gray Purple
Row 10: Gray Gray Purple Orange Yellow Pink Gray Red Orange Yellow Pink Gray Gray Gray Gray
Row 11: Red Gray Gray Gray Purple Gray Orange Yellow Pink Purple Gray Red Gray Gray Gray
Row 12: Yellow Pink Gray Gray Gray Gray Gray Purple Gray Gray Orange Yellow Pink Gray Gray
Row 13: Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray
Row 14: Red Gray Gray Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red
Row 15: Yellow Pink Gray Gray Gray Orange Yellow Pink Gray Gray Orange Yellow Pink Orange Yellow
Row 16: Purple Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Purple Red Gray Purple
Row 17: Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Orange Yellow Pink Gray
Row 18: Red Gray Orange Yellow Pink Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray
Row 19: Yellow Pink Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Red Gray Gray
Row 20: Purple Gray Gray Gray Red Gray Gray Gray Gray Red Gray Orange Yellow Pink Gray
Row 21: Gray Gray Gray Orange Yellow Pink Gray Gray Orange Yellow Pink Gray Purple Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Black Green Black Black Black Black Black Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black
Row 3: Black Black Black Black Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Green Black Black Green Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Green Black Black Black Black Black Black Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Green Black Black Black Green Black Black Black Green Black Black Black Green Black Black Black Black Black Black Green Black Black Green
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Green Pink Black Black Black Orange Green Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Red Black Black
Black Purple Black Black Red Black Black Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Green Pink Black
Black Black Black Orange Green Pink Black Black Red Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Red Purple Black Black
Black Black Black Black Purple Black Black Orange Green Pink Orange Green Pink Black Black Black Black Black Black Black Black Black Black Orange Green Pink Black Red
Black Black Black Black Black Black Black Black Purple Black Black Purple Black Black Black Black Black Black Black Black Black Black Black Black Purple Black Orange Green
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Red Black Black Black Black Black Black Purple
Black Black Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Orange Green Pink Black Black Black Black Black Red
Black Black Black Black Black Black Orange Green Pink Black Black Black Black Black Black Black Black Black Black Black Purple Black Black Black Black Black Orange Green
Black Black Black Black Black Black Black Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Purple
Black Black Black Black Black Red Black Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Red Black Orange Green Pink Black Black Black Black Orange Green Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Orange Green Pink Black Purple Black Black Black Black Black Black Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Orange Green Pink Red Black Black Black Red Black Black Black Red Black Black Black Red Black Black Black Black Black Black Red Black Black Red
Black Black Black Purple Orange Green Pink Black Orange Green Pink Black Orange Green Pink Black Orange Green Pink Black Black Black Black Orange Green Pink Orange Green
Black Black Black Black Black Purple Black Black Black Purple Black Black Black Purple Black Black Black Purple Black Black Black Black Black Black Purple Black Black Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Purple Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Black Orange Purple Orange Orange Brown Orange Gray Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Blue Orange Orange Orange Orange Orange Green Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Purple Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Purple Orange Green Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Blue Orange Blue Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Purple Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Purple Orange Blue Orange Purple Orange Orange
Row 12: Orange Orange Blue Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange
Row 13: Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Blue Orange Red Orange Blue Orange Orange
Row 14: Orange Orange Blue Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange Orange Blue Orange Purple Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Purple Orange Green Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Black Orange Purple Orange Orange Brown Orange Gray Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Blue Orange Orange Orange Orange Orange Green Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Purple Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Purple Orange Green Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Blue Orange Blue Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Purple Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Purple Orange Blue Orange Purple Orange Orange
Row 12: Orange Orange Blue Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Purple Orange Orange Orange
Row 13: Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Blue Orange Red Orange Blue Orange Orange
Row 14: Orange Orange Blue Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Purple Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Purple Orange Blue Orange Purple Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Purple Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Gray Pink Pink Pink Gray Pink
Row 13: Pink Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Yellow Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Gray Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 27: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 28: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Purple Pink Purple Pink Purple Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Purple Pink Yellow Pink Purple Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Purple Pink Purple Pink Purple Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Gray Pink Pink Pink Gray Pink
Row 13: Pink Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Pink Pink Yellow Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Gray Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 27: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 28: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Example 3
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Red Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Pink Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Red Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Pink Black Black Black Black Gray Black Gray Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Red Black Gray Black Black Black Black Black Black Orange Black Black Black Black Black Black
Row 7: Black Black Black Pink Black Pink Black Pink Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Gray Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Pink Black Red Black Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Orange Black Purple Black Orange Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Pink Black Pink Black Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Red Black Gray Black Red Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Pink Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Red Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Pink Black Black Black Black Gray Black Gray Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Red Black Gray Black Red Black Black Black Black Orange Black Black Black Black Black Black
Row 7: Black Black Black Pink Black Pink Black Pink Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Gray Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Pink Black Red Black Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Orange Black Purple Black Orange Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Pink Black Pink Black Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Black Pink Gray Pink Black Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Gray Pink Purple Pink Gray Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Red Pink Red Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Black Pink Gray Pink Black Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Blue Pink Pink Pink Blue Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Blue Pink Pink Pink Blue Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Black Pink Gray Pink Black Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Red Pink Red Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Gray Pink Purple Pink Gray Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Red Pink Red Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Black Pink Gray Pink Black Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Pink Pink Pink Blue Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Blue Pink Pink Pink Blue Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Blue Brown Gray Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Black
Row 5: Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Orange
Row 6: Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Black
Row 7: Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Black
Output:
Row 1: Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown
Row 3: Brown Gray Brown Brown Brown Blue Brown Gray Brown Brown Brown
Row 4: Brown Brown Brown Brown Black Blue Brown Brown Brown Brown Black
Row 5: Brown Brown Brown Brown Orange Blue Brown Brown Brown Brown Orange
Row 6: Brown Brown Brown Brown Black Blue Brown Brown Brown Brown Black
Row 7: Brown Brown Brown Brown Black Blue Brown Brown Brown Brown Black
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue
Row 5: Red Red Red Red Red Red Red
Row 6: Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Brown Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Yellow
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Brown Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Yellow
Row 5: Red Red Red Red Red Red Red
Row 6: Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Brown Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Yellow
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Yellow Brown Yellow
Row 2: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Yellow Yellow Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Yellow Brown Yellow Yellow Brown
Row 4: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Yellow Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Yellow Brown
Row 6: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Yellow Brown Brown Yellow Yellow Brown
Row 7: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Yellow Brown Brown
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Yellow Brown Yellow Black Brown Brown Brown Yellow Brown Yellow Black Brown Brown Brown Yellow Brown Yellow
Row 2: Brown Brown Yellow Yellow Brown Brown Black Brown Brown Yellow Yellow Brown Brown Black Brown Brown Yellow Yellow Brown Brown
Row 3: Brown Yellow Brown Yellow Yellow Brown Black Brown Yellow Brown Yellow Yellow Brown Black Brown Yellow Brown Yellow Yellow Brown
Row 4: Yellow Brown Brown Brown Brown Brown Black Yellow Brown Brown Brown Brown Brown Black Yellow Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Yellow Brown Black Brown Brown Brown Brown Yellow Brown Black Brown Brown Brown Brown Yellow Brown
Row 6: Yellow Brown Brown Yellow Yellow Brown Black Yellow Brown Brown Yellow Yellow Brown Black Yellow Brown Brown Yellow Yellow Brown
Row 7: Brown Brown Brown Yellow Brown Brown Black Brown Brown Brown Yellow Brown Brown Black Brown Brown Brown Yellow Brown Brown
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Brown Brown Brown Yellow Brown Yellow Black Brown Brown Brown Yellow Brown Yellow Black Brown Brown Brown Yellow Brown Yellow
Row 10: Brown Brown Yellow Yellow Brown Brown Black Brown Brown Yellow Yellow Brown Brown Black Brown Brown Yellow Yellow Brown Brown
Row 11: Brown Yellow Brown Yellow Yellow Brown Black Brown Yellow Brown Yellow Yellow Brown Black Brown Yellow Brown Yellow Yellow Brown
Row 12: Yellow Brown Brown Brown Brown Brown Black Yellow Brown Brown Brown Brown Brown Black Yellow Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Yellow Brown Black Brown Brown Brown Brown Yellow Brown Black Brown Brown Brown Brown Yellow Brown
Row 14: Yellow Brown Brown Yellow Yellow Brown Black Yellow Brown Brown Yellow Yellow Brown Black Yellow Brown Brown Yellow Yellow Brown
Row 15: Brown Brown Brown Yellow Brown Brown Black Brown Brown Brown Yellow Brown Brown Black Brown Brown Brown Yellow Brown Brown
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Brown Brown Brown Yellow Brown Yellow Black Brown Brown Brown Yellow Brown Yellow Black Brown Brown Brown Yellow Brown Yellow
Row 18: Brown Brown Yellow Yellow Brown Brown Black Brown Brown Yellow Yellow Brown Brown Black Brown Brown Yellow Yellow Brown Brown
Row 19: Brown Yellow Brown Yellow Yellow Brown Black Brown Yellow Brown Yellow Yellow Brown Black Brown Yellow Brown Yellow Yellow Brown
Row 20: Yellow Brown Brown Brown Brown Brown Black Yellow Brown Brown Brown Brown Brown Black Yellow Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Yellow Brown Black Brown Brown Brown Brown Yellow Brown Black Brown Brown Brown Brown Yellow Brown
Row 22: Yellow Brown Brown Yellow Yellow Brown Black Yellow Brown Brown Yellow Yellow Brown Black Yellow Brown Brown Yellow Yellow Brown
Row 23: Brown Brown Brown Yellow Brown Brown Black Brown Brown Brown Yellow Brown Brown Black Brown Brown Brown Yellow Brown Brown
Here is the input grid for the test example:
Input:
Row 1: Blue Purple Blue
Row 2: Gray Blue Blue
Row 3: Blue Blue Blue
Row 4: Red Red Red
Row 5: Blue Blue Blue
Row 6: Blue Blue Blue
Row 7: Blue Blue Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Purple Blue
Gray Blue Blue
Blue Blue Blue
Red Red Red
Blue Purple Blue
Gray Blue Blue
Blue Blue Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Gray Black Gray Black
Row 2: Black Black Gray Black Gray Black
Row 3: Black Black Gray Black Gray Black
Row 4: Gray Gray Gray Gray Gray Gray
Row 5: Black Black Gray Black Gray Black
Row 6: Black Black Gray Black Gray Black
Row 7: Gray Gray Gray Gray Gray Gray
Row 8: Black Black Gray Black Gray Black
Row 9: Black Black Gray Black Gray Black
Row 10: Black Black Gray Black Gray Black
Row 11: Black Black Gray Black Gray Black
Row 12: Black Black Gray Black Gray Black
Row 13: Black Black Gray Black Gray Black
Row 14: Black Black Gray Black Gray Black
Output:
Row 1: Black Black Gray Red Gray Black
Row 2: Black Black Gray Red Gray Black
Row 3: Black Black Gray Red Gray Black
Row 4: Gray Gray Gray Gray Gray Gray
Row 5: Yellow Yellow Gray Pink Gray Green
Row 6: Yellow Yellow Gray Pink Gray Green
Row 7: Gray Gray Gray Gray Gray Gray
Row 8: Black Black Gray Blue Gray Black
Row 9: Black Black Gray Blue Gray Black
Row 10: Black Black Gray Blue Gray Black
Row 11: Black Black Gray Blue Gray Black
Row 12: Black Black Gray Blue Gray Black
Row 13: Black Black Gray Blue Gray Black
Row 14: Black Black Gray Blue Gray Black
Example 2
Input:
Row 1: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple
Row 2: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple
Row 5: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple
Row 6: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple
Row 7: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple
Row 8: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple
Row 9: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple
Row 10: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple
Row 11: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple
Row 12: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple
Row 13: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple
Row 14: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple
Row 17: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple
Row 18: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple
Row 19: Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple
Output:
Row 1: Purple Purple Purple Gray Red Red Red Gray Purple Purple
Row 2: Purple Purple Purple Gray Red Red Red Gray Purple Purple
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Yellow Yellow Yellow Gray Pink Pink Pink Gray Green Green
Row 5: Yellow Yellow Yellow Gray Pink Pink Pink Gray Green Green
Row 6: Yellow Yellow Yellow Gray Pink Pink Pink Gray Green Green
Row 7: Yellow Yellow Yellow Gray Pink Pink Pink Gray Green Green
Row 8: Yellow Yellow Yellow Gray Pink Pink Pink Gray Green Green
Row 9: Yellow Yellow Yellow Gray Pink Pink Pink Gray Green Green
Row 10: Yellow Yellow Yellow Gray Pink Pink Pink Gray Green Green
Row 11: Yellow Yellow Yellow Gray Pink Pink Pink Gray Green Green
Row 12: Yellow Yellow Yellow Gray Pink Pink Pink Gray Green Green
Row 13: Yellow Yellow Yellow Gray Pink Pink Pink Gray Green Green
Row 14: Yellow Yellow Yellow Gray Pink Pink Pink Gray Green Green
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Purple Purple Purple Gray Blue Blue Blue Gray Purple Purple
Row 17: Purple Purple Purple Gray Blue Blue Blue Gray Purple Purple
Row 18: Purple Purple Purple Gray Blue Blue Blue Gray Purple Purple
Row 19: Purple Purple Purple Gray Blue Blue Blue Gray Purple Purple
Example 3
Input:
Row 1: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 2: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 3: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 4: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 5: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 6: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 7: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 8: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 9: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 10: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 13: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 14: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 15: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 16: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 19: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 20: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 21: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 22: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Purple Purple Purple Purple
Row 2: Purple Purple Purple Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Purple Purple Purple Purple
Row 3: Purple Purple Purple Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Purple Purple Purple Purple
Row 4: Purple Purple Purple Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Purple Purple Purple Purple
Row 5: Purple Purple Purple Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Purple Purple Purple Purple
Row 6: Purple Purple Purple Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Purple Purple Purple Purple
Row 7: Purple Purple Purple Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Purple Purple Purple Purple
Row 8: Purple Purple Purple Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Purple Purple Purple Purple
Row 9: Purple Purple Purple Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Purple Purple Purple Purple
Row 10: Purple Purple Purple Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Purple Purple Purple Purple
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Yellow Yellow Yellow Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Green Green Green Green
Row 13: Yellow Yellow Yellow Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Green Green Green Green
Row 14: Yellow Yellow Yellow Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Green Green Green Green
Row 15: Yellow Yellow Yellow Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Green Green Green Green
Row 16: Yellow Yellow Yellow Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Green Green Green Green
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Purple Purple Purple Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Purple Purple Purple Purple
Row 19: Purple Purple Purple Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Purple Purple Purple Purple
Row 20: Purple Purple Purple Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Purple Purple Purple Purple
Row 21: Purple Purple Purple Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Purple Purple Purple Purple
Row 22: Purple Purple Purple Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 23: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 24: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 25: Black Black Black Gray Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Black Black Gray Red Red Red Red Red Red Red Red Gray Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Gray Red Red Red Red Red Red Red Red Gray Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Gray Red Red Red Red Red Red Red Red Gray Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Gray Red Red Red Red Red Red Red Red Gray Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Gray Red Red Red Red Red Red Red Red Gray Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Gray Red Red Red Red Red Red Red Red Gray Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Gray Red Red Red Red Red Red Red Red Gray Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Gray Red Red Red Red Red Red Red Red Gray Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Gray Red Red Red Red Red Red Red Red Gray Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Gray Red Red Red Red Red Red Red Red Gray Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Gray Red Red Red Red Red Red Red Red Gray Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Gray Red Red Red Red Red Red Red Red Gray Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Gray Red Red Red Red Red Red Red Red Gray Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Gray Red Red Red Red Red Red Red Red Gray Black Black Black Black Black Black Black Black Black Black Black
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Yellow Yellow Yellow Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Green Green Green Green Green Green Green Green Green Green Green
Yellow Yellow Yellow Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Green Green Green Green Green Green Green Green Green Green Green
Yellow Yellow Yellow Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Green Green Green Green Green Green Green Green Green Green Green
Yellow Yellow Yellow Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Green Green Green Green Green Green Green Green Green Green Green
Yellow Yellow Yellow Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Green Green Green Green Green Green Green Green Green Green Green
Yellow Yellow Yellow Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Green Green Green Green Green Green Green Green Green Green Green
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Black Black Black Gray Blue Blue Blue Blue Blue Blue Blue Blue Gray Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Gray Blue Blue Blue Blue Blue Blue Blue Blue Gray Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Gray Blue Blue Blue Blue Blue Blue Blue Blue Gray Black Black Black Black Black Black Black Black Black Black Black |
Subsets and Splits