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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 Black Orange Black Purple Purple
Row 2: Black Purple Purple Orange Purple Orange
Output:
Row 1: Purple Black Orange Black Purple Purple Purple Purple Black Orange Black Purple
Row 2: Black Purple Purple Orange Purple Orange Orange Purple Orange Purple Purple Black
Example 2
Input:
Row 1: Black Black Brown Black Purple Black Pink Black
Row 2: Black Black Yellow Blue Brown Black Black Black
Row 3: Black Black Red Black Brown Brown Brown Brown
Row 4: Orange Orange Black Black Orange Green Blue Black
Row 5: Black Black Black Purple Black Orange Green Green
Row 6: Black Pink Black Yellow Brown Black Black Black
Row 7: Black Green Brown Black Black Purple Black Blue
Row 8: Red Green Pink Black Black Purple Black Brown
Row 9: Brown Black Purple Black Black Black Black Purple
Row 10: Black Black Black Black Black Brown Black Purple
Row 11: Black Black Black Purple Green Purple Brown Black
Row 12: Blue Black Brown Black Black Red Black Black
Row 13: Black Black Black Black Black Orange Black Black
Row 14: Black Black Black Black Black Blue Blue Purple
Row 15: Black Black Orange Black Yellow Red Black Brown
Row 16: Purple Black Brown Black Pink Black Green Black
Row 17: Black Black Black Green Black Black Black Orange
Row 18: Black Black Blue Black Black Black Black Brown
Row 19: Blue Blue Brown Black Brown Black Orange Black
Row 20: Black Green Black Purple Black Green Purple Blue
Row 21: Black Green Purple Black Orange Black Black Yellow
Output:
Row 1: Black Black Brown Black Purple Black Pink Black Black Pink Black Purple Black Brown Black Black
Row 2: Black Black Yellow Blue Brown Black Black Black Black Black Black Brown Blue Yellow Black Black
Row 3: Black Black Red Black Brown Brown Brown Brown Brown Brown Brown Brown Black Red Black Black
Row 4: Orange Orange Black Black Orange Green Blue Black Black Blue Green Orange Black Black Orange Orange
Row 5: Black Black Black Purple Black Orange Green Green Green Green Orange Black Purple Black Black Black
Row 6: Black Pink Black Yellow Brown Black Black Black Black Black Black Brown Yellow Black Pink Black
Row 7: Black Green Brown Black Black Purple Black Blue Blue Black Purple Black Black Brown Green Black
Row 8: Red Green Pink Black Black Purple Black Brown Brown Black Purple Black Black Pink Green Red
Row 9: Brown Black Purple Black Black Black Black Purple Purple Black Black Black Black Purple Black Brown
Row 10: Black Black Black Black Black Brown Black Purple Purple Black Brown Black Black Black Black Black
Row 11: Black Black Black Purple Green Purple Brown Black Black Brown Purple Green Purple Black Black Black
Row 12: Blue Black Brown Black Black Red Black Black Black Black Red Black Black Brown Black Blue
Row 13: Black Black Black Black Black Orange Black Black Black Black Orange Black Black Black Black Black
Row 14: Black Black Black Black Black Blue Blue Purple Purple Blue Blue Black Black Black Black Black
Row 15: Black Black Orange Black Yellow Red Black Brown Brown Black Red Yellow Black Orange Black Black
Row 16: Purple Black Brown Black Pink Black Green Black Black Green Black Pink Black Brown Black Purple
Row 17: Black Black Black Green Black Black Black Orange Orange Black Black Black Green Black Black Black
Row 18: Black Black Blue Black Black Black Black Brown Brown Black Black Black Black Blue Black Black
Row 19: Blue Blue Brown Black Brown Black Orange Black Black Orange Black Brown Black Brown Blue Blue
Row 20: Black Green Black Purple Black Green Purple Blue Blue Purple Green Black Purple Black Green Black
Row 21: Black Green Purple Black Orange Black Black Yellow Yellow Black Black Orange Black Purple Green Black
Example 3
Input:
Row 1: Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Purple Red Red Red Red Red
Row 3: Red Red Purple Red Red Red Red Red Red
Row 4: 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
Row 2: Red Red Red Purple Red Red Red Red Red Red Red Red Red Red Purple Red Red Red
Row 3: Red Red Purple Red Red Red Red Red Red Red Red Red Red Red Red Purple Red Red
Row 4: 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
Row 2: Brown
Row 3: Green
Row 4: Gray
Row 5: Brown
Row 6: Black
Row 7: Brown
Row 8: Pink
Row 9: Brown
Row 10: 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
Brown Brown
Green Green
Gray Gray
Brown Brown
Black Black
Brown Brown
Pink Pink
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: Black Black Black Black Black Black 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 Blue 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 Blue Pink Blue 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 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 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 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 Black Black Black Black Black Yellow Black Black
Row 8: 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 Yellow Yellow Yellow Black
Row 9: Black Black Black Black Black Black Black Blue Orange Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Yellow Yellow Pink Yellow Yellow
Row 10: 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
Row 11: Black Black Black Black Black Black Pink Black Black Black Black Black Black Black Yellow Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Pink Blue Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black 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 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 Green 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 Green Green 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 Green Green Pink 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 Black Black Black Black Black Green Green Black Black Black
Row 18: Black Black Black Black Black Black Black Yellow Yellow Yellow Brown Yellow Yellow Yellow Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black
Row 19: Black Black Black Brown Black Black Black Black Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Brown Green Black Black Black Black Black Yellow Yellow Yellow Black Black Black Brown Brown Orange Brown Brown Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Brown Black Black Black Black Black Black Yellow Black Black Black Black Black Brown Brown Brown 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 Black Black Brown 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 Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black Black Pink Black Black
Row 2: Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Pink Black Black
Row 3: Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Blue Pink Blue Black Black Black Black Black Pink Black Black
Row 4: 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 Pink Black Black
Row 5: 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 Pink Black Black
Row 6: 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 Pink Black Black
Row 7: 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 Yellow Black Black
Row 8: 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 Yellow Yellow Yellow Black
Row 9: Black Black Black Black Black Black Black Blue Orange Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Yellow Yellow Pink Yellow Yellow
Row 10: 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
Row 11: Black Black Black Black Black Black Pink Black Black Black Black Black Black Black Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Blue Blue Blue Blue Blue Pink Blue Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black 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 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 Green 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 Green Green Black Black Black
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 Green Green Pink 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 Black Black Black Black Black Green Green Black Black Black
Row 18: Black Black Black Black Black Black Black Yellow Yellow Yellow Brown Yellow Yellow Yellow Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black
Row 19: Black Black Black Brown Black Black Black Black Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Green Green Brown Green Black Black Black Black Black Yellow Yellow Yellow Black Black Black Brown Brown Orange Brown Brown Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Brown Black Black Black Black Black Black Yellow Black Black Black Black Black Brown Brown Brown Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Red Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red 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
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Red Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue 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 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 Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Blue Blue Blue Blue Blue Purple Blue Blue Blue
Row 11: Blue Blue Blue Red Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Blue Blue Blue Blue Red Purple Blue Blue
Row 12: Blue Blue Red Purple Red Blue Blue Blue Purple Purple Purple Red Purple Purple Purple Blue Blue Blue Purple 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
Output:
Row 1: Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Red Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Purple Red Purple Purple Purple Purple
Row 3: Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Red Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Red Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Pink Red Pink Pink Pink Pink Pink Pink
Row 7: Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Red Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Blue Blue Blue Blue Blue Purple Blue Blue Blue
Row 11: Blue Blue Blue Red Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Blue Blue Blue Blue Red Purple Red Red
Row 12: Blue Blue Red Purple Red Blue Blue Blue Purple Purple Purple Red Purple Purple Purple Blue Blue Blue Purple 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
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
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
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Yellow Gray Orange Gray Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Gray Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray 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
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
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
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Black Black Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Black Black Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Yellow Brown Yellow Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Gray Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Orange Orange Orange Gray Gray Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Black Gray Gray Gray Orange Orange Gray Gray Gray Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Gray Gray Gray Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange
Row 21: Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Orange Orange Orange
Row 22: Orange Blue Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Gray Orange
Row 23: Orange Orange Blue Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Gray
Row 24: Orange Orange Orange Orange Black Black Black Orange Gray Black Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange
Row 25: Orange Orange Orange Black Black Brown Black Black Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 26: Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Black Blue Blue Orange Orange
Row 27: Blue Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Orange Orange Orange
Row 28: Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Brown Gray Orange Orange Blue Orange Orange Orange Orange
Row 29: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Black Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Black Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Black Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Black Orange Orange Orange Gray Yellow Gray Orange Gray Orange Orange
Row 5: Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Yellow Gray Yellow
Row 6: Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange
Row 7: Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Black Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Black Orange Orange Orange Orange Black Black Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Black Orange Orange Orange Orange Brown Black Black Brown Brown Brown
Row 13: Orange Orange Orange Orange Orange Brown Orange Orange Orange Yellow Orange Orange Black Orange Orange Orange Orange Black Black Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Brown Orange Orange Yellow Brown Yellow Orange Black Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Gray Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Gray Gray Gray Gray Gray Orange Orange Orange Gray Gray Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Brown Orange Orange Orange Gray Gray Gray Black Gray Gray Gray Orange Orange Gray Gray Gray Orange Orange
Row 19: Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Gray Gray Gray Brown
Row 20: Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange
Row 21: Orange Orange Blue Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Orange Orange Orange
Row 22: Yellow Blue Yellow Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Gray Orange
Row 23: Orange Orange Blue Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Gray
Row 24: Orange Orange Orange Orange Black Black Black Orange Gray Black Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange
Row 25: Orange Orange Orange Black Black Brown Black Black Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 26: Orange Blue Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Blue Blue Black Blue Blue Orange Orange
Row 27: Blue Black Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Orange Orange Orange
Row 28: Orange Blue Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Gray Brown Gray Orange Orange Blue Orange Orange Orange Orange
Row 29: Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Gray Orange Orange Orange Black Orange Orange Orange Orange
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
Row 2: 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 Brown Black Black
Row 4: Black Black Green Black Black Black Black Black Black Black Black Black Black Black Black Brown Purple Brown Black
Row 5: Black Green Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Green 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
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Gray Gray Gray Red Gray Gray Gray
Row 9: Black Black Black Black Black Black Black Black Black Black Red Black Black Gray Gray Gray Gray Gray Black
Row 10: Black Black Black Black Black Gray Black Black Black Red Red Red Black Black Gray Gray Gray Black Black
Row 11: Black Black Black Black Gray Purple Gray Black Red Red Purple Red Red Black Black Gray Black Black Black
Row 12: 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
Row 14: 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 Purple Black Black Black Black Purple Black Black Black Black Black Purple Black Black
Black Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Black Purple Black Black
Black Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Black Brown Black Black
Black Black Green Black Black Purple Black Black Black Black Purple Black Black Black Black Brown Purple Brown Black
Purple Green Purple Black Black Purple Black Black Black Black Purple Black Black Black Black Black Black Black Black
Black Black Green Black Black Purple Black Black Black Black Purple Black Black Black Black Black Black Black Black
Black Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Black Black Black Black
Black Black Black Black Black Purple Black Black Black Black Purple Black Gray Gray Gray Red Gray Gray Gray
Black Black Black Black Black Purple Black Black Black Black Red Black Black Gray Gray Gray Gray Gray Black
Black Black Black Black Black Gray Black Black Black Red Red Red Black Black Gray Gray Gray Black Black
Black Black Black Black Gray Purple Gray Black Red Red Purple Red Red Black Black Gray 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 Red Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Red 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 Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Blue Brown Brown Blue Brown Purple Brown Brown Brown Brown Brown Blue Brown Pink
Row 3: Brown Blue Brown Blue Brown Purple Blue Brown Brown Blue Blue Blue Brown Brown
Row 4: Blue Brown Brown Brown Blue Brown Brown Blue Blue Brown Brown Blue Brown Brown
Row 5: Brown Brown Brown Brown Blue Purple Brown Blue Brown Blue Purple Brown Brown Blue
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Purple Brown Brown
Row 7: Brown Brown Brown Blue Brown Brown Purple Blue Brown Brown Blue Brown Brown Brown
Row 8: Brown Blue Blue Brown Blue Blue Brown Blue Pink Brown Brown Brown Brown Blue
Output:
Row 1: Blue Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Blue
Row 2: Blue Brown Brown Blue Brown Purple Brown Brown Brown Brown Brown Blue Brown Pink Pink Brown Blue Brown Brown Brown Brown Brown Purple Brown Blue Brown Brown Blue
Row 3: Brown Blue Brown Blue Brown Purple Blue Brown Brown Blue Blue Blue Brown Brown Brown Brown Blue Blue Blue Brown Brown Blue Purple Brown Blue Brown Blue Brown
Row 4: Blue Brown Brown Brown Blue Brown Brown Blue Blue Brown Brown Blue Brown Brown Brown Brown Blue Brown Brown Blue Blue Brown Brown Blue Brown Brown Brown Blue
Row 5: Brown Brown Brown Brown Blue Purple Brown Blue Brown Blue Purple Brown Brown Blue Blue Brown Brown Purple Blue Brown Blue Brown Purple Blue Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Purple Brown Brown Brown Brown Purple Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Blue Brown Brown Purple Blue Brown Brown Blue Brown Brown Brown Brown Brown Brown Blue Brown Brown Blue Purple Brown Brown Blue Brown Brown Brown
Row 8: Brown Blue Blue Brown Blue Blue Brown Blue Pink Brown Brown Brown Brown Blue Blue Brown Brown Brown Brown Pink Blue Brown Blue Blue Brown Blue Blue Brown
Example 2
Input:
Row 1: Black Yellow
Row 2: Yellow Black
Row 3: Black Yellow
Row 4: Yellow Black
Row 5: Yellow Yellow
Row 6: Black Yellow
Row 7: Black Yellow
Row 8: Black Yellow
Row 9: Black Black
Row 10: Yellow Black
Row 11: Black Black
Row 12: Black Yellow
Row 13: Black Yellow
Row 14: Black Yellow
Row 15: Black Yellow
Row 16: Yellow Black
Row 17: Yellow Black
Row 18: Yellow Yellow
Output:
Row 1: Black Yellow Yellow Black
Row 2: Yellow Black Black Yellow
Row 3: Black Yellow Yellow Black
Row 4: Yellow Black Black Yellow
Row 5: Yellow Yellow Yellow Yellow
Row 6: Black Yellow Yellow Black
Row 7: Black Yellow Yellow Black
Row 8: Black Yellow Yellow Black
Row 9: Black Black Black Black
Row 10: Yellow Black Black Yellow
Row 11: Black Black Black Black
Row 12: Black Yellow Yellow Black
Row 13: Black Yellow Yellow Black
Row 14: Black Yellow Yellow Black
Row 15: Black Yellow Yellow Black
Row 16: Yellow Black Black Yellow
Row 17: Yellow Black Black Yellow
Row 18: Yellow Yellow Yellow Yellow
Example 3
Input:
Row 1: Black Gray Gray Gray Gray Gray Brown Yellow
Row 2: Brown Black Green Purple Black Gray Gray Brown
Row 3: Red Brown Gray Gray Gray Brown Gray Gray
Row 4: Gray Brown Brown Gray Green Yellow Gray Gray
Row 5: Gray Gray Purple Gray Gray Gray Gray Brown
Row 6: Gray Black Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Green Gray Brown Gray Gray Yellow
Row 8: Gray Green Gray Gray Gray Gray Black Brown
Row 9: Pink Orange Gray Purple Gray Gray Gray Gray
Row 10: Pink Orange Gray Orange Gray Gray Yellow Gray
Row 11: Gray Pink Purple Brown Gray Gray Blue Gray
Row 12: Gray Gray Green Gray Green Gray Purple Gray
Row 13: Gray Green Gray Gray Pink Gray Gray Green
Row 14: Yellow Black Gray Gray Gray Gray Pink Blue
Row 15: Gray Black Yellow Orange Gray Gray Blue Gray
Row 16: Black Gray Black Yellow Gray Gray Gray Gray
Row 17: Gray Gray Gray Pink Gray Yellow Gray Yellow
Row 18: Gray Gray Gray Gray Gray Pink Gray Gray
Row 19: Red Gray Pink Gray Green Gray Orange Gray
Output:
Row 1: Black Gray Gray Gray Gray Gray Brown Yellow Yellow Brown Gray Gray Gray Gray Gray Black
Row 2: Brown Black Green Purple Black Gray Gray Brown Brown Gray Gray Black Purple Green Black Brown
Row 3: Red Brown Gray Gray Gray Brown Gray Gray Gray Gray Brown Gray Gray Gray Brown Red
Row 4: Gray Brown Brown Gray Green Yellow Gray Gray Gray Gray Yellow Green Gray Brown Brown Gray
Row 5: Gray Gray Purple Gray Gray Gray Gray Brown Brown Gray Gray Gray Gray Purple Gray Gray
Row 6: Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray
Row 7: Gray Gray Green Gray Brown Gray Gray Yellow Yellow Gray Gray Brown Gray Green Gray Gray
Row 8: Gray Green Gray Gray Gray Gray Black Brown Brown Black Gray Gray Gray Gray Green Gray
Row 9: Pink Orange Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Orange Pink
Row 10: Pink Orange Gray Orange Gray Gray Yellow Gray Gray Yellow Gray Gray Orange Gray Orange Pink
Row 11: Gray Pink Purple Brown Gray Gray Blue Gray Gray Blue Gray Gray Brown Purple Pink Gray
Row 12: Gray Gray Green Gray Green Gray Purple Gray Gray Purple Gray Green Gray Green Gray Gray
Row 13: Gray Green Gray Gray Pink Gray Gray Green Green Gray Gray Pink Gray Gray Green Gray
Row 14: Yellow Black Gray Gray Gray Gray Pink Blue Blue Pink Gray Gray Gray Gray Black Yellow
Row 15: Gray Black Yellow Orange Gray Gray Blue Gray Gray Blue Gray Gray Orange Yellow Black Gray
Row 16: Black Gray Black Yellow Gray Gray Gray Gray Gray Gray Gray Gray Yellow Black Gray Black
Row 17: Gray Gray Gray Pink Gray Yellow Gray Yellow Yellow Gray Yellow Gray Pink Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray
Row 19: Red Gray Pink Gray Green Gray Orange Gray Gray Orange Gray Green Gray Pink Gray Red
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Gray Purple Black
Row 3: Yellow Gray Yellow Yellow Yellow Green Orange Yellow
Row 4: Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Blue Yellow Blue
Row 6: Yellow Orange Yellow Yellow Pink Yellow Orange Gray
Row 7: Yellow Orange Blue Gray Orange Yellow Yellow Yellow
Row 8: Black Yellow Black Blue Black Green Yellow Gray
Row 9: Yellow Yellow Yellow Yellow Yellow Black Orange Yellow
Row 10: Yellow Yellow Yellow Orange Yellow Yellow Orange Orange
Row 11: Green Yellow Yellow Gray Yellow Gray 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 Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Gray Purple Black Black Purple Gray Yellow Yellow Yellow Yellow Yellow
Yellow Gray Yellow Yellow Yellow Green Orange Yellow Yellow Orange Green Yellow Yellow Yellow Gray Yellow
Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Blue Yellow Blue Blue Yellow Blue Yellow Yellow Yellow Yellow Yellow
Yellow Orange Yellow Yellow Pink Yellow Orange Gray Gray Orange Yellow Pink Yellow Yellow Orange Yellow
Yellow Orange Blue Gray Orange Yellow Yellow Yellow Yellow Yellow Yellow Orange Gray Blue Orange Yellow
Black Yellow Black Blue Black Green Yellow Gray Gray Yellow Green Black Blue Black Yellow Black
Yellow Yellow Yellow Yellow Yellow Black Orange Yellow Yellow Orange Black Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Orange Yellow Yellow Orange Orange Orange Orange Yellow Yellow Orange Yellow Yellow Yellow
Green Yellow Yellow Gray Yellow Gray Yellow Yellow Yellow Yellow Gray Yellow Gray Yellow Yellow 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 Blue Blue Blue Pink Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Pink
Row 2: Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue
Row 3: Blue Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Pink Blue Blue Blue
Row 4: Blue Pink Pink Blue Blue Blue Pink Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Pink
Row 5: Blue Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Pink Blue Blue Blue
Row 6: Blue Pink Pink Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 7: Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Pink Blue Blue Blue
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 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 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 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 Black Black Black Black Black Black
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Pink 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 Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink 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 Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Pink 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 Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue
Row 21: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue
Row 22: Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Pink 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 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 Blue Blue
Row 3: Blue Blue Black 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 Blue
Row 4: Blue Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Black Blue Blue Blue
Row 5: Blue Black Black Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Blue Blue Black Blue Blue Black Blue Black Blue Blue Blue
Row 6: Blue Black Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Blue Blue Black Blue Blue Black Blue Black Blue Blue Black
Row 7: Blue Black Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Blue Blue Black Blue Blue Black Blue Black Blue Blue 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 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 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 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 Black Black Black Black Black Black
Row 12: Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Black Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 13: Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 14: Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 15: Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black 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 Black 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 Black 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 Black 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 Black 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 Black 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 Blue Blue
Example 2
Input:
Row 1: Brown Brown Brown Brown Orange Orange Orange Orange Green Brown Brown Brown Brown Green Green
Row 2: Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Green Brown Brown Green Brown
Row 3: Brown Brown Brown Brown Orange Orange Orange Orange Green Green Brown Brown Brown Green Green
Row 4: Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown
Row 5: Green Green Brown Brown Orange Orange Orange Orange Green Green Green Green Brown Green Brown
Row 6: Brown Brown Brown Brown Orange Orange Orange Orange Green Green Green Green Brown Green Green
Row 7: Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown
Row 10: Green Brown Green Green Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown
Row 4: Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown
Row 6: Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown
Row 7: Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown
Example 3
Input:
Row 1: Blue Blue Black Black Black Blue Blue Blue
Row 2: Blue Blue Black Black Black Brown Blue Brown
Row 3: Blue Blue Black Black Black Blue Blue Blue
Row 4: Blue Blue Black Black Black Brown Blue Blue
Row 5: Blue Blue Black Black Black Blue Blue Blue
Row 6: Blue Blue Black Black Black Blue Blue Brown
Row 7: Brown Blue Black Black Black Blue Blue Blue
Row 8: Blue Blue Black Black Black Brown Blue Brown
Row 9: Brown Blue Black Black Black Brown Brown Blue
Row 10: Blue Brown Black Black Black Blue Blue Blue
Row 11: Blue Blue Black Black Black Blue Blue Blue
Row 12: Blue Blue Black Black Black Blue Blue Blue
Row 13: Blue Brown Black Black Black Blue Blue Brown
Row 14: Blue Blue Black Black Black Blue Blue Blue
Row 15: Brown Blue Black Black Black Blue Brown Blue
Row 16: Blue Blue Black Black Black Blue Blue Blue
Row 17: Brown Blue Black Black Black Blue Blue Blue
Row 18: Blue Blue Black Black Black Blue Blue Blue
Row 19: Blue Blue Black Black Black Blue Blue Blue
Row 20: Blue Brown Black Black Black Blue Blue Blue
Row 21: Blue Blue Black Black Black Blue Blue Blue
Row 22: Blue Blue Black Black Black Blue Blue Blue
Row 23: Blue Blue Black Black Black Blue Blue Blue
Row 24: Brown Blue Black Black Black Blue Blue Blue
Row 25: Blue Blue Black Black Black Blue Brown Brown
Output:
Row 1: Blue Blue Black Black Black Blue Blue Blue
Row 2: Blue Blue Black Black Black Black Black Blue
Row 3: Blue Blue Black Black Black Blue Blue Blue
Row 4: Blue Blue Black Black Black Black Blue Blue
Row 5: Blue Blue Black Black Black Blue Blue Blue
Row 6: Blue Blue Black Black Black Black Blue Blue
Row 7: Blue Black Black Black Black Blue Blue Blue
Row 8: Blue Blue Black Black Black Black Black Blue
Row 9: Blue Black Black Black Black Black Black Blue
Row 10: Blue Black Black Black Black Blue Blue Blue
Row 11: Blue Blue Black Black Black Blue Blue Blue
Row 12: Blue Blue Black Black Black Blue Blue Blue
Row 13: Blue Black Black Black Black Black Blue Blue
Row 14: Blue Blue Black Black Black Blue Blue Blue
Row 15: Blue Black Black Black Black Black Blue Blue
Row 16: Blue Blue Black Black Black Blue Blue Blue
Row 17: Blue Black Black Black Black Blue Blue Blue
Row 18: Blue Blue Black Black Black Blue Blue Blue
Row 19: Blue Blue Black Black Black Blue Blue Blue
Row 20: Blue Black Black Black Black Blue Blue Blue
Row 21: Blue Blue Black Black Black Blue Blue Blue
Row 22: Blue Blue Black Black Black Blue Blue Blue
Row 23: Blue Blue Black Black Black Blue Blue Blue
Row 24: Blue Black Black Black Black Blue Blue Blue
Row 25: Blue Blue Black Black Black Black Black Blue
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Red Red Gray Gray Red Gray Red Red Red Red Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Black Black Black Gray Gray Red Gray Gray Red Red Gray Gray Red
Row 7: Red Red Gray Red Red Red Red Red Red Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Black Black Black Red Red Gray Gray Red Gray Red Gray Red Red
Row 10: Red Red Red Gray Red Red Red Red Red Red Black Black Black Black Black Black Gray Gray Gray Gray Red Red Gray Gray Red Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Black Black Black Gray Red Gray Gray Red Red Red Red Gray Red
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Black Black Black Gray Gray Red Red Red Gray Gray Red Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Red Red Gray Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Red Red Gray Gray Gray Red Red Red Red Red Black Black Black Black Black Black Red Gray Red Red Red Red Red Red Red 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 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 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 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 Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Black Black 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 Black Black Black Black Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray
Gray Gray Black Black Black 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 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 Black Black Black Black Black Black Black Black Black Black Black Black Gray Gray Gray Gray
Gray Black Black Black Black Black Black Black 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 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 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 Black 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 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 Black Black Black Black Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Black Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black 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: 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 Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Blue Blue Blue 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
Row 8: 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
Row 10: Red Red Red Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Gray Gray Gray Gray Gray Gray Gray 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
Row 14: 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 Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red
Row 16: Red Red Red Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red
Row 17: Red Red Red Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green 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
Row 19: 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
Row 21: 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
Row 23: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 24: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 25: Red Red Red Red Red Red Red 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 Red Red Red Red Red Red Red
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: 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
Row 2: Red Red Red Red Red Red Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Blue Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Blue Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Blue Blue Blue 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
Row 8: 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
Row 10: Red Red Red Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Gray Red Gray Red Gray Red Gray Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Gray Gray Gray Gray Gray Gray Gray 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
Row 14: 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 Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red
Row 16: Red Red Red Red Green Red Green Red Green Red Green Red Green Red Green Red Green Red Green Red Green Red
Row 17: Red Red Red Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green 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
Row 19: 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
Row 21: 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
Row 23: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 24: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 25: Red Red Red Red Red Red Red 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 Red Red Red Red Red Red Red
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: 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 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 Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 3: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 4: Green Green Green Yellow Yellow Yellow Yellow Red Red Red Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 5: Green Green Green Yellow Yellow Yellow Yellow Red Red Red Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 6: Green Green Green Yellow Yellow Yellow Yellow Red Red Red Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 7: Green Green Green Yellow Yellow Yellow Yellow Red Red Red Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 8: Green Green Green Yellow Yellow Yellow Yellow Red Red Red Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 9: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 10: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 11: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Black Black Black Gray Gray Gray Yellow
Row 12: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Black Black Black Gray Gray Gray Yellow
Row 13: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Black Black Black Gray Gray Gray Yellow
Row 14: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 15: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 16: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 17: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 18: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 19: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink 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
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 Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 3: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Yellow Black Yellow Black Yellow Yellow Yellow Yellow
Row 4: Green Yellow Green Yellow Yellow Yellow Yellow Red Red Red Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 5: Green Green Green Yellow Yellow Yellow Yellow Red Yellow Red Pink Yellow Pink Yellow Black Yellow Black Yellow Yellow Yellow Yellow
Row 6: Green Yellow Green Yellow Yellow Yellow Yellow Red Red Red Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 7: Green Green Green Yellow Yellow Yellow Yellow Red Yellow Red Pink Yellow Pink Yellow Black Yellow Black Yellow Yellow Yellow Yellow
Row 8: Green Yellow Green Yellow Yellow Yellow Yellow Red Red Red Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 9: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Yellow Black Yellow Black Yellow Yellow Yellow Yellow
Row 10: Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 11: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Yellow Black Yellow Black Gray Gray Gray Yellow
Row 12: Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Black Black Black Gray Yellow Gray Yellow
Row 13: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Yellow Black Yellow Black Gray Gray Gray Yellow
Row 14: Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 15: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Yellow Black Yellow Black Yellow Yellow Yellow Yellow
Row 16: Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 17: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Yellow Black Yellow Black Yellow Yellow Yellow Yellow
Row 18: Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 19: Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink 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
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink
Row 2: Pink Pink Blue Blue Blue Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink
Row 3: Pink Pink Blue Blue Blue Pink Pink Yellow Yellow Yellow Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink
Row 4: Pink Pink Blue Blue Blue Pink Pink Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Pink Pink
Row 5: Pink Pink Blue Blue Blue Pink Pink Yellow Yellow Yellow Gray Gray Gray Pink Pink Pink Pink Pink Orange Orange Orange Pink Pink
Row 6: Pink Pink Blue Blue Blue Pink Pink Green Green Green Gray Gray Gray Pink Pink Pink Pink Pink Orange Orange Orange Pink Pink
Row 7: Pink Pink Blue Blue Blue Pink Pink Green Green Green Gray Gray Gray Pink Pink Pink Pink Pink Orange Orange Orange Pink Pink
Row 8: Pink Pink Blue Blue Blue Pink Pink Green Green Green Gray Gray Gray Pink Pink Pink Pink Pink Orange Orange Orange Pink Pink
Row 9: Pink Pink Blue Blue Blue Pink Pink Green Green Green Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Blue Blue Blue Pink Pink Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Blue Blue Blue Pink Pink Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Blue Blue Blue Pink Pink Green Green Green Pink Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Brown Brown Brown Brown Brown Brown Brown 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
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink
Row 2: Pink Pink Blue Blue Blue Pink Pink Pink Pink Pink Red Pink Red Pink Red Pink Red Pink Red Pink Pink Pink Pink
Row 3: Pink Pink Blue Pink Blue Pink Pink Yellow Yellow Yellow Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink
Row 4: Pink Pink Blue Blue Blue Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Pink Pink
Row 5: Pink Pink Blue Pink Blue Pink Pink Yellow Yellow Yellow Gray Gray Gray Pink Pink Pink Pink Pink Orange Pink Orange Pink Pink
Row 6: Pink Pink Blue Blue Blue Pink Pink Green Green Green Gray Pink Gray Pink Pink Pink Pink Pink Orange Orange Orange Pink Pink
Row 7: Pink Pink Blue Pink Blue Pink Pink Green Pink Green Gray Gray Gray Pink Pink Pink Pink Pink Orange Pink Orange Pink Pink
Row 8: Pink Pink Blue Blue Blue Pink Pink Green Green Green Gray Pink Gray Pink Pink Pink Pink Pink Orange Orange Orange Pink Pink
Row 9: Pink Pink Blue Pink Blue Pink Pink Green Pink Green Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Blue Blue Blue Pink Pink Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Blue Pink Blue Pink Pink Green Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Blue Blue Blue Pink Pink Green Green Green Pink Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Green Pink Green Pink Brown Pink Brown Pink Brown Pink Brown Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Brown Brown Brown Brown Brown Brown Brown 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
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 Purple Purple Purple Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Pink Pink
Row 5: Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Pink Pink
Row 6: Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Pink Pink
Row 7: Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Pink Pink
Row 10: Pink Pink Pink Black Black Black Pink Pink Pink Pink Purple Purple Purple Pink Pink
Row 11: Pink Pink Pink Black Black Black Pink Pink Pink Pink Purple Purple Purple Pink Pink
Row 12: Pink Pink Pink Black Black Black Pink Pink Pink Pink Purple Purple Purple Pink Pink
Row 13: Pink Pink Pink Black Black Black Pink Pink Pink Pink Purple Purple Purple Pink Pink
Row 14: Pink Pink Pink Black Black Black Pink Pink Pink Pink Purple Purple Purple Pink Pink
Row 15: Pink Pink Pink Black Black Black Pink Pink Pink Pink Purple Purple Purple Pink Pink
Row 16: Pink Pink Pink Black Black Black Pink Pink Pink Pink Purple Purple Purple Pink Pink
Row 17: Pink Pink Pink Black Black Black Pink Pink Pink Pink Purple Purple Purple Pink Pink
Row 18: Pink Pink Pink Black Black Black Pink Pink Pink Pink Purple Purple Purple Pink Pink
Row 19: Pink Pink Pink Black Black Black Pink Pink Pink Pink Purple Purple Purple Pink Pink
Row 20: Pink Pink Pink Black Black Black Pink Pink Pink Pink Purple Purple Purple Pink Pink
Row 21: Pink Pink Pink Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Black Black Black 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
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 Purple Purple Purple Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Purple Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Pink Pink
Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Purple Pink Purple Pink Pink
Pink Pink Pink Blue Pink Blue Pink Blue Pink Blue Purple Purple Purple Pink Pink
Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Purple Pink Purple Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Purple Pink Pink
Pink Pink Pink Black Black Black Pink Pink Pink Pink Purple Purple Purple Pink Pink
Pink Pink Pink Black Pink Black Pink Pink Pink Pink Purple Pink Purple Pink Pink
Pink Pink Pink Black Black Black Pink Pink Pink Pink Purple Purple Purple Pink Pink
Pink Pink Pink Black Pink Black Pink Pink Pink Pink Purple Pink Purple Pink Pink
Pink Pink Pink Black Black Black Pink Pink Pink Pink Purple Purple Purple Pink Pink
Pink Pink Pink Black Pink Black Pink Pink Pink Pink Purple Pink Purple Pink Pink
Pink Pink Pink Black Black Black Pink Pink Pink Pink Purple Purple Purple Pink Pink
Pink Pink Pink Black Pink Black Pink Pink Pink Pink Purple Pink Purple Pink Pink
Pink Pink Pink Black Black Black Pink Pink Pink Pink Purple Purple Purple Pink Pink
Pink Pink Pink Black Pink Black Pink Pink Pink Pink Purple Pink Purple Pink Pink
Pink Pink Pink Black Black Black Pink Pink Pink Pink Purple Purple Purple Pink Pink
Pink Pink Pink Black Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Black Black 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 |
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 Purple Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Purple Gray Gray Green Gray Gray Gray
Row 4: Purple Purple Purple Purple Purple Gray Gray Green Gray Gray Gray
Row 5: Purple Gray Gray Gray Purple Gray Gray Green Green Gray Gray
Row 6: Purple Gray Gray Gray Gray Black Gray Gray Gray Black Gray
Row 7: Purple Gray Gray Gray Gray Black Black Black Black Black Gray
Row 8: Purple Gray Black Black Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Black Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Black Gray Gray Black Black Black Black Black Black
Row 11: Gray Gray Black Black Black Gray Gray Gray Gray Gray Black
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black
Row 13: Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Black
Row 14: Gray Purple Gray Gray Purple Gray Gray Black Black Black Gray
Row 15: Gray Purple Purple Purple Purple Gray Gray Black Gray Gray Gray
Row 16: Gray Purple Gray Gray Gray Gray Gray Black Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Black Black Black Black Black Black
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray
Row 20: Gray Purple Gray Gray Gray Gray Gray Gray Green Green Green
Row 21: Gray Purple Gray Gray Gray Gray Gray Gray Gray Green Gray
Row 22: Gray Purple Gray Gray Gray Gray Gray Gray Gray Green Gray
Row 23: Gray Purple Gray Gray Gray Gray Gray Green Green Green Gray
Output:
Row 1: Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Red Gray Gray Blue Gray Gray Gray
Row 4: Red Red Red Red Red Gray Gray Blue Gray Gray Gray
Row 5: Red Gray Gray Gray Red Gray Gray Blue Blue Gray Gray
Row 6: Red Gray Gray Gray Gray Pink Gray Gray Gray Pink Gray
Row 7: Red Gray Gray Gray Gray Pink Pink Pink Pink Pink Gray
Row 8: Red Gray Pink Pink Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Pink Gray Gray Blue Blue Blue Blue Blue Blue
Row 11: Gray Gray Pink Pink Pink Gray Gray Gray Gray Gray Blue
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue
Row 13: Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Blue
Row 14: Gray Red Gray Gray Red Gray Gray Red Red Red Gray
Row 15: Gray Red Red Red Red Gray Gray Red Gray Gray Gray
Row 16: Gray Red Gray Gray Gray Gray Gray Red Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Red Red Red Red Red Red
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray
Row 20: Gray Blue Gray Gray Gray Gray Gray Gray Red Red Red
Row 21: Gray Blue Gray Gray Gray Gray Gray Gray Gray Red Gray
Row 22: Gray Blue Gray Gray Gray Gray Gray Gray Gray Red Gray
Row 23: Gray Blue Gray Gray Gray Gray Gray Red Red Red Gray
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Green Purple Purple Green Purple Purple Purple
Row 2: Purple Purple Black Black Black Black Black Black Purple Green Green Purple Purple Purple Brown Purple Purple Purple Green Green Green Green Purple Purple Purple
Row 3: Purple Purple Black Purple Purple Purple Purple Black Purple Green Purple Purple Purple Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Black Purple Purple Purple Purple Black Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green Green
Row 5: Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green
Row 6: Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Brown Purple Purple Green Green Green Green Green Green Purple Purple Purple Green
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Green Purple Purple Purple Green
Row 8: Purple Purple Purple Black Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple Green Purple Purple Purple Purple
Row 9: Brown Brown Purple Black Black Black Black Black Purple Purple Purple Green Green Green Purple Purple Green Purple Purple Purple Green Purple Purple Purple Purple
Row 10: Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Green Purple Purple Purple Green Purple Purple Purple Purple
Row 11: Brown Purple Purple Green Green Green Green Green Purple Brown Brown Purple Green Green Purple Purple Green Purple Purple Purple Green Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Black Black Purple Purple
Row 13: Purple Green Green Green Green Green Purple Purple Purple Purple Brown Purple Brown Brown Brown Purple Green Green Green Purple Purple Black Purple Green Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Brown Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Green Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Brown Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Purple
Row 16: Purple Purple Purple Purple Purple Purple Green Green Purple Brown Brown Purple Brown Purple Purple Purple Purple Green Green Purple Purple Purple Purple Green Purple
Row 17: Purple Green Green Green Green Purple Green Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Green Purple
Row 18: Purple Green Purple Purple Green Purple Green Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Green Purple Purple Purple Purple Purple Green Purple
Row 19: Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Pink Purple Purple Pink Purple Purple Purple
Row 2: Purple Purple Pink Pink Pink Pink Pink Pink Purple Pink Pink Purple Purple Purple Blue Purple Purple Purple Pink Pink Pink Pink Purple Purple Purple
Row 3: Purple Purple Pink Purple Purple Purple Purple Pink Purple Pink Purple Purple Purple Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Pink Purple Purple Purple Purple Pink Purple Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Blue Blue Blue Blue
Row 5: Purple Purple Pink Purple Purple Purple Purple Pink Purple Purple Purple Purple Red Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue
Row 6: Purple Purple Pink Purple Purple Purple Purple Pink Purple Purple Purple Purple Red Purple Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Blue
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Purple Purple Purple Purple Purple Blue Purple Purple Purple Blue
Row 8: Purple Purple Purple Pink Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Purple Blue Purple Purple Purple Purple
Row 9: Blue Blue Purple Pink Pink Pink Pink Pink Purple Purple Purple Pink Pink Pink Purple Purple Pink Purple Purple Purple Blue Purple Purple Purple Purple
Row 10: Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Pink Purple Purple Purple Blue Purple Purple Purple Purple
Row 11: Blue Purple Purple Red Red Red Red Red Purple Pink Pink Purple Pink Pink Purple Purple Pink Purple Purple Purple Blue Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Blue Blue Purple Purple
Row 13: Purple Red Red Red Red Red Purple Purple Purple Purple Pink Purple Pink Pink Pink Purple Pink Pink Pink Purple Purple Blue Purple Red Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Pink Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Red Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Pink Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Purple
Row 16: Purple Purple Purple Purple Purple Purple Red Red Purple Pink Pink Purple Pink Purple Purple Purple Purple Pink Pink Purple Purple Purple Purple Red Purple
Row 17: Purple Pink Pink Pink Pink Purple Red Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Red Purple
Row 18: Purple Pink Purple Purple Pink Purple Red Purple Purple Purple Purple Purple Pink Pink Pink Purple Purple Pink Purple Purple Purple Purple Purple Red Purple
Row 19: Purple Purple Purple Purple Purple Red Red Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Purple Purple Purple
Example 3
Input:
Row 1: Black Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Green Green Green Purple Purple Purple Brown Brown Brown Brown Brown Purple
Row 2: Black Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Green Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple
Row 3: Black Purple Purple Yellow Yellow Purple Purple Purple Purple Black Purple Purple Green Purple Purple Purple Brown Brown Purple Purple Purple Purple Purple Purple
Row 4: Black Purple Purple Purple Yellow Purple Black Black Purple Purple Purple Purple Green Purple Purple Purple Purple Brown Purple Yellow Yellow Yellow Yellow Purple
Row 5: Black Black Purple Purple Yellow Purple Purple Black Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple
Row 6: Purple Purple Brown Purple Purple Purple Purple Black Purple Brown Purple Purple Green Green Green Green Green Purple Purple Purple Purple Purple Yellow Purple
Row 7: Purple Purple Brown Purple Black Black Black Black Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow
Row 8: Purple Purple Brown Brown Purple Purple Purple Purple Purple Brown Brown Brown Brown 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 Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Black Black Black Black Black Black Purple
Row 12: Purple Purple Brown Purple Purple Purple Black Black Black Black Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Black Purple
Row 13: Purple Purple Brown Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Black Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Brown Brown Brown Brown Brown Purple Purple Purple Purple Black Purple
Row 15: Brown Brown Brown Brown Brown Purple Purple Purple Purple Black Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Brown Purple Purple Purple Purple Black Purple Yellow Purple Purple Green Green Green Green Purple Purple Purple Green Green Green
Row 17: Purple Purple Purple Purple Brown Purple Purple Black Black Black Purple Yellow Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Green
Row 18: Purple Purple Brown Brown Brown Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Purple Green Purple Purple Purple Purple Purple Green Green
Row 19: Purple Purple Purple Purple Purple Purple Black Black Black Black Purple Purple Purple Purple Purple Purple Green Purple Green Green Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Yellow Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Green Purple Purple Green Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Yellow Purple Green Green Purple Green Purple Green Green Purple
Row 22: Purple Purple Purple Purple Yellow Purple Purple Purple Yellow Purple Purple Yellow Yellow Yellow Yellow Purple Purple Purple Green Green Purple Green Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Blue Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Purple Pink Pink Pink Purple Purple Purple Blue Blue Blue Blue Blue Purple
Row 2: Blue Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Pink Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple
Row 3: Blue Purple Purple Blue Blue Purple Purple Purple Purple Blue Purple Purple Pink Purple Purple Purple Blue Blue Purple Purple Purple Purple Purple Purple
Row 4: Blue Purple Purple Purple Blue Purple Pink Pink Purple Purple Purple Purple Pink Purple Purple Purple Purple Blue Purple Red Red Red Red Purple
Row 5: Blue Blue Purple Purple Blue Purple Purple Pink Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple
Row 6: Purple Purple Blue Purple Purple Purple Purple Pink Purple Blue Purple Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Red Purple
Row 7: Purple Purple Blue Purple Pink Pink Pink Pink Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red
Row 8: Purple Purple Blue Blue Purple Purple Purple Purple Purple Blue Blue Blue Blue 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 Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Blue Blue Blue Blue Blue Blue Purple
Row 12: Purple Purple Blue Purple Purple Purple Pink Pink Pink Pink Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 13: Purple Purple Blue Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple Blue Purple
Row 15: Pink Pink Pink Pink Pink Purple Purple Purple Purple Pink Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Pink Purple Purple Purple Purple Pink Purple Blue Purple Purple Red Red Red Red Purple Purple Purple Pink Pink Pink
Row 17: Purple Purple Purple Purple Pink Purple Purple Pink Pink Pink Purple Blue Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Pink
Row 18: Purple Purple Pink Pink Pink Purple Purple Purple Purple Purple Purple Blue Blue Blue Blue Purple Red Purple Purple Purple Purple Purple Pink Pink
Row 19: Purple Purple Purple Purple Purple Purple Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Red Purple Pink Pink Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Red Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Red Purple Purple Pink Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Red Red Red Red Red Purple Purple Purple Purple Purple Blue Purple Red Red Purple Pink Purple Blue Blue Purple
Row 22: Purple Purple Purple Purple Red Purple Purple Purple Red Purple Purple Blue Blue Blue Blue Purple Purple Purple Pink Pink Purple Blue Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Red 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: Purple Purple Purple Green Green Green Green Green Green Green Green Green Green Green Purple Purple Purple Purple Purple Purple Green
Row 2: Purple Green Green Green Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Purple Green
Row 3: Purple Green Black Black Green Green Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Black Green Green Green Black Black Black Black Black Black Green Green Purple Green Green Green Green Green
Row 5: Brown Green Green Black Green Green Green Green Green Green Green Black Green Green Green Purple Green Green Green Green Green
Row 6: Brown Green Green Black Green Green Black Black Black Black Black Black Green Green Green Purple Green Green Green Green Purple
Row 7: Brown Green Green Black Green Green Green Green Green Green Green Green Green Green Green Purple Green Green Green Green Purple
Row 8: Brown Green Green Black Green Yellow Yellow Green Green Green Green Green Green Green Green Purple Purple Purple Purple Purple Purple
Row 9: Brown Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Brown Brown Brown Brown Brown Green Yellow Green Green Green Brown Brown Green Green Green Green Green Black Black Black Green
Row 11: Green Green Green Green Green Green Yellow Green Green Green Brown Green Yellow Yellow Green Green Green Black Green Black Green
Row 12: Green Green Green Green Green Yellow Yellow Green Green Green Brown Green Green Yellow Green Green Green Green Green Green Green
Row 13: Green Green Green Purple Purple Green Green Green Green Green Brown Green Green Yellow Green Purple Purple Purple Purple Purple Purple
Row 14: Brown Green Green Green Purple Green Green Green Green Green Brown Green Yellow Yellow Green Green Green Purple Green Green Green
Row 15: Brown Brown Green Green Purple Green Green Green Green Green Brown Brown Green Green Green Green Green Purple Green Green Green
Row 16: Green Green Green Green Purple Green Purple Purple Purple Green Green Green Green Green Green Green Green Purple Green Green Green
Row 17: Green Green Green Purple Purple Green Purple Green Green Green Green Green Green Green Green Purple Purple Purple 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 Blue Blue Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Blue Blue Green
Blue Green Green Green Blue Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Blue Green
Blue Green Blue Blue Green Green Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Blue Green Green Green Red Red Red Red Red Red Green Green Pink Green Green Green Green Green
Blue Green Green Blue Green Green Green Green Green Green Green Red Green Green Green Pink Green Green Green Green Green
Blue Green Green Blue Green Green Red Red Red Red Red Red Green Green Green Pink Green Green Green Green Pink
Blue Green Green Blue Green Green Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Pink
Blue Green Green Blue Green Pink Pink Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink
Blue Green Green Green Green Green Pink Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Blue Blue Blue Blue Blue Green Pink Green Green Green Pink Pink Green Green Green Green Green Pink Pink Pink Green
Green Green Green Green Green Green Pink Green Green Green Pink Green Pink Pink Green Green Green Pink Green Pink Green
Green Green Green Green Green Pink Pink Green Green Green Pink Green Green Pink Green Green Green Green Green Green Green
Green Green Green Pink Pink Green Green Green Green Green Pink Green Green Pink Green Red Red Red Red Red Red
Blue Green Green Green Pink Green Green Green Green Green Pink Green Pink Pink Green Green Green Red Green Green Green
Blue Blue Green Green Pink Green Green Green Green Green Pink Pink Green Green Green Green Green Red Green Green Green
Green Green Green Green Pink Green Blue Blue Blue Green Green Green Green Green Green Green Green Red Green Green Green
Green Green Green Pink Pink Green Blue Green Green Green Green Green Green Green Green Red Red Red 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: Brown Gray Red Gray Blue Green Red Red Pink Pink Red Red Brown Red Brown Blue Pink Blue Green Blue Gray Red Green Gray Pink Red Red Red Blue
Row 2: Gray Brown Blue Brown Gray Green Blue Brown Green Red Gray Green Pink Blue Green Brown Green Pink Gray Green Brown Blue Red Red Brown Red Red Brown Green
Row 3: Pink Red Gray Pink Pink Pink Red Brown Pink Gray Blue Green Blue Red Pink Blue Gray Pink Gray Brown Green Green Brown Red Pink Blue Pink Green Gray
Row 4: Blue Red Green Blue Green Brown Pink Green Gray Gray Gray Blue Red Brown Green Red Blue Brown Gray Gray Green Red Red Gray Blue Green Blue Blue Green
Row 5: Green Brown Pink Gray Blue Green Pink Brown Gray Green Gray Green Green Blue Red Red Green Pink Brown Green Brown Green Brown Red Pink Blue Blue Blue Pink
Row 6: Blue Green Brown Brown Red Brown Gray Brown Red Red Brown Blue Green Pink Pink Green Gray Blue Blue Brown Gray Red Gray Brown Red Pink Blue Red Pink
Row 7: Blue Blue Green Red Green Brown Blue Pink Red Red Red Red Green Red Pink Gray Brown Gray Red Red Gray Blue Pink Blue Gray Pink Pink Gray Blue
Row 8: Red Brown Pink Pink Blue Green Blue Gray Brown Red Green Pink Brown Blue Green Pink Pink Gray Pink Blue Pink Brown Gray Blue Red Pink Red Pink Pink
Row 9: Green Pink Gray Brown Pink Gray Gray Gray Gray Brown Gray Green Pink Gray Blue Green Brown Green Pink Green Blue Pink Gray Blue Pink Brown Pink Gray Gray
Row 10: Pink Blue Gray Brown Blue Red Green Brown Blue Blue Brown Blue Pink Pink Pink Gray Green Brown Green Pink Red Red Brown Blue Gray Green Gray Gray Gray
Row 11: Red Gray Red Pink Green Red Gray Blue Brown Gray Blue Brown Brown Green Blue Gray Gray Red Gray Green Red Red Green Gray Pink Gray Brown Gray Brown
Row 12: Red Pink Brown Gray Blue Red Brown Gray Gray Red Blue Pink Brown Red Blue Pink Brown Pink Gray Pink Brown Green Blue Brown Green Gray Gray Gray Green
Row 13: Red Red Green Green Red Blue Brown Gray Gray Pink Blue Blue Green Blue Pink Green Brown Red Green Gray Pink Pink Blue Red Green Pink Green Gray Blue
Row 14: Brown Brown Brown Brown Gray Red Pink Gray Gray Gray Blue Blue Brown Brown Pink Green Brown Brown Brown Green Brown Blue Brown Brown Blue Pink Brown Pink Gray
Row 15: Gray Pink Gray Blue Brown Brown Brown Brown Brown Pink Blue Gray Blue Gray Pink Red Gray Gray Pink Gray Pink Pink Blue Gray Brown Green Red Brown Brown
Row 16: Gray Red Blue Brown Green Pink Red Gray Blue Brown Red Red Green Green Pink Blue Red Pink Green Red Green Gray Blue Gray Gray Brown Green Gray Brown
Row 17: Pink Brown Brown Red Red Red Gray Red Blue Green Brown Green Brown Brown Red Red Brown Brown Blue Gray Blue Brown Brown Blue Brown Blue Red Blue Red
Row 18: Green Pink Red Gray Blue Red Green Blue Gray Gray Brown Blue Green Pink Green Brown Blue Green Red Gray Pink Green Pink Green Brown Blue Gray Blue Blue
Row 19: Blue Blue Red Green Blue Green Blue Green Red Pink Gray Green Pink Gray Blue Brown Red Brown Red Pink Red Green Brown Blue Gray Gray Blue Green Brown
Row 20: Red Brown Brown Gray Gray Red Green Brown Pink Pink Red Red Brown Red Gray Blue Brown Red Red Green Pink Green Gray Gray Red Blue Brown Red Gray
Row 21: Gray Blue Gray Pink Pink Brown Green Blue Green Gray Green Brown Blue Gray Green Pink Brown Blue Pink Green Blue Gray Green Green Green Pink Red Brown Gray
Output:
Row 1: Purple Blue Pink Blue Gray Yellow Pink Pink Red Red Pink Pink Purple Pink Purple Gray Red Gray Yellow Gray Blue Pink Yellow Blue Red Pink Pink Pink Gray
Row 2: Blue Purple Gray Purple Blue Yellow Gray Purple Yellow Pink Blue Yellow Red Gray Yellow Purple Yellow Red Blue Yellow Purple Gray Pink Pink Purple Pink Pink Purple Yellow
Row 3: Red Pink Blue Red Red Red Pink Purple Red Blue Gray Yellow Gray Pink Red Gray Blue Red Blue Purple Yellow Yellow Purple Pink Red Gray Red Yellow Blue
Row 4: Gray Pink Yellow Gray Yellow Purple Red Yellow Blue Blue Blue Gray Pink Purple Yellow Pink Gray Purple Blue Blue Yellow Pink Pink Blue Gray Yellow Gray Gray Yellow
Row 5: Yellow Purple Red Blue Gray Yellow Red Purple Blue Yellow Blue Yellow Yellow Gray Pink Pink Yellow Red Purple Yellow Purple Yellow Purple Pink Red Gray Gray Gray Red
Row 6: Gray Yellow Purple Purple Pink Purple Blue Purple Pink Pink Purple Gray Yellow Red Red Yellow Blue Gray Gray Purple Blue Pink Blue Purple Pink Red Gray Pink Red
Row 7: Gray Gray Yellow Pink Yellow Purple Gray Red Pink Pink Pink Pink Yellow Pink Red Blue Purple Blue Pink Pink Blue Gray Red Gray Blue Red Red Blue Gray
Row 8: Pink Purple Red Red Gray Yellow Gray Blue Purple Pink Yellow Red Purple Gray Yellow Red Red Blue Red Gray Red Purple Blue Gray Pink Red Pink Red Red
Row 9: Yellow Red Blue Purple Red Blue Blue Blue Blue Purple Blue Yellow Red Blue Gray Yellow Purple Yellow Red Yellow Gray Red Blue Gray Red Purple Red Blue Blue
Row 10: Red Gray Blue Purple Gray Pink Yellow Purple Gray Gray Purple Gray Red Red Red Blue Yellow Purple Yellow Red Pink Pink Purple Gray Blue Yellow Blue Blue Blue
Row 11: Pink Blue Pink Red Yellow Pink Blue Gray Purple Blue Gray Purple Purple Yellow Gray Blue Blue Pink Blue Yellow Pink Pink Yellow Blue Red Blue Purple Blue Purple
Row 12: Pink Red Purple Blue Gray Pink Purple Blue Blue Pink Gray Red Purple Pink Gray Red Purple Red Blue Red Purple Yellow Gray Purple Yellow Blue Blue Blue Yellow
Row 13: Pink Pink Yellow Yellow Pink Gray Purple Blue Blue Red Gray Gray Yellow Gray Red Yellow Purple Pink Yellow Blue Red Red Gray Pink Yellow Red Yellow Blue Gray
Row 14: Purple Purple Purple Purple Blue Pink Red Blue Blue Blue Gray Gray Purple Purple Red Yellow Purple Purple Purple Yellow Purple Gray Purple Purple Gray Red Purple Red Blue
Row 15: Blue Red Blue Gray Purple Purple Purple Purple Purple Red Gray Blue Gray Blue Red Pink Blue Blue Red Blue Red Red Gray Blue Purple Yellow Pink Purple Purple
Row 16: Blue Pink Gray Purple Yellow Red Pink Blue Gray Purple Pink Pink Yellow Yellow Red Gray Pink Red Yellow Pink Yellow Blue Gray Blue Blue Purple Yellow Blue Purple
Row 17: Red Purple Purple Pink Pink Pink Blue Pink Gray Yellow Purple Yellow Purple Purple Pink Pink Purple Purple Gray Blue Gray Purple Purple Gray Purple Gray Pink Gray Pink
Row 18: Yellow Red Pink Blue Gray Pink Yellow Gray Blue Blue Purple Gray Yellow Red Yellow Purple Gray Yellow Pink Blue Red Yellow Red Yellow Purple Gray Blue Gray Gray
Row 19: Gray Gray Pink Yellow Gray Yellow Gray Yellow Pink Red Blue Yellow Red Blue Gray Purple Pink Purple Pink Red Pink Yellow Purple Gray Blue Blue Gray Yellow Purple
Row 20: Pink Purple Purple Blue Blue Pink Yellow Purple Red Red Pink Pink Purple Pink Blue Gray Purple Pink Pink Yellow Red Yellow Blue Blue Pink Gray Purple Pink Blue
Row 21: Blue Gray Blue Red Red Purple Yellow Gray Yellow Blue Yellow Purple Gray Blue Yellow Red Purple Gray Red Yellow Gray Blue Yellow Yellow Yellow Red Pink Purple Blue
Example 2
Input:
Row 1: Green Green Purple Blue Blue Purple Blue Blue Blue Blue Green Purple Green Blue Green Green
Row 2: Purple Blue Blue Purple Purple Purple Blue Green Purple Blue Blue Blue Purple Blue Green Purple
Row 3: Purple Blue Green Purple Blue Blue Green Purple Purple Green Purple Blue Blue Purple Green Green
Row 4: Blue Blue Purple Purple Purple Purple Green Green Purple Green Green Green Green Green Blue Green
Row 5: Purple Purple Purple Green Green Blue Blue Green Green Green Green Purple Green Blue Green Purple
Row 6: Purple Green Blue Blue Green Blue Purple Purple Purple Purple Blue Green Purple Green Purple Green
Row 7: Green Blue Purple Green Green Blue Blue Green Green Blue Blue Blue Blue Purple Green Purple
Row 8: Blue Purple Purple Blue Blue Blue Green Purple Blue Blue Blue Purple Blue Purple Purple Blue
Row 9: Green Green Green Green Green Purple Purple Green Blue Blue Blue Purple Blue Green Purple Blue
Row 10: Purple Purple Blue Green Blue Blue Purple Blue Blue Purple Blue Purple Purple Blue Blue Purple
Row 11: Green Blue Green Blue Blue Green Purple Purple Green Green Blue Blue Purple Blue Green Purple
Row 12: Purple Green Green Purple Purple Green Blue Green Blue Green Purple Purple Green Green Blue Purple
Row 13: Green Green Purple Purple Green Blue Green Blue Blue Green Blue Purple Green Purple Green Blue
Row 14: Blue Purple Blue Purple Purple Green Purple Green Purple Blue Green Green Blue Purple Blue Purple
Row 15: Purple Green Blue Purple Purple Blue Purple Green Blue Blue Purple Blue Purple Green Green Blue
Row 16: Purple Purple Green Blue Green Green Green Purple Purple Purple Blue Purple Purple Green Purple Blue
Row 17: Blue Purple Purple Green Blue Blue Blue Blue Blue Green Purple Blue Blue Green Purple Purple
Row 18: Blue Green Blue Blue Blue Green Blue Blue Purple Purple Blue Purple Purple Green Green Blue
Row 19: Blue Blue Purple Purple Purple Blue Purple Blue Purple Green Blue Purple Green Blue Green Purple
Row 20: Green Green Blue Green Purple Green Purple Green Blue Purple Green Green Blue Green Purple Purple
Row 21: Purple Blue Green Purple Blue Purple Green Blue Green Purple Green Green Green Blue Green Blue
Output:
Row 1: Yellow Yellow Brown Gray Gray Brown Gray Gray Gray Gray Yellow Brown Yellow Gray Yellow Yellow
Row 2: Brown Gray Gray Brown Brown Brown Gray Yellow Brown Gray Gray Gray Brown Gray Yellow Brown
Row 3: Brown Gray Yellow Brown Gray Gray Yellow Brown Brown Yellow Brown Gray Gray Brown Yellow Yellow
Row 4: Gray Gray Brown Brown Brown Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Gray Yellow
Row 5: Brown Brown Brown Yellow Yellow Gray Gray Yellow Yellow Yellow Yellow Brown Yellow Gray Yellow Brown
Row 6: Brown Yellow Gray Gray Yellow Gray Brown Brown Brown Brown Gray Yellow Brown Yellow Brown Yellow
Row 7: Yellow Gray Brown Yellow Yellow Gray Gray Yellow Yellow Gray Gray Gray Gray Brown Yellow Brown
Row 8: Gray Brown Brown Gray Gray Gray Yellow Brown Gray Gray Gray Brown Gray Brown Brown Gray
Row 9: Yellow Yellow Yellow Yellow Yellow Brown Brown Yellow Gray Gray Gray Brown Gray Yellow Brown Gray
Row 10: Brown Brown Gray Yellow Gray Gray Brown Gray Gray Brown Gray Brown Brown Gray Gray Brown
Row 11: Yellow Gray Yellow Gray Gray Yellow Brown Brown Yellow Yellow Gray Gray Brown Gray Yellow Brown
Row 12: Brown Yellow Yellow Brown Brown Yellow Gray Yellow Gray Yellow Brown Brown Yellow Yellow Gray Brown
Row 13: Yellow Yellow Brown Brown Yellow Gray Yellow Gray Gray Yellow Gray Brown Yellow Brown Yellow Gray
Row 14: Gray Brown Gray Brown Brown Yellow Brown Yellow Brown Gray Yellow Yellow Gray Brown Gray Brown
Row 15: Brown Yellow Gray Brown Brown Gray Brown Yellow Gray Gray Brown Gray Brown Yellow Yellow Gray
Row 16: Brown Brown Yellow Gray Yellow Yellow Yellow Brown Brown Brown Gray Brown Brown Yellow Brown Gray
Row 17: Gray Brown Brown Yellow Gray Gray Gray Gray Gray Yellow Brown Gray Gray Yellow Brown Brown
Row 18: Gray Yellow Gray Gray Gray Yellow Gray Gray Brown Brown Gray Brown Brown Yellow Yellow Gray
Row 19: Gray Gray Brown Brown Brown Gray Brown Gray Brown Yellow Gray Brown Yellow Gray Yellow Brown
Row 20: Yellow Yellow Gray Yellow Brown Yellow Brown Yellow Gray Brown Yellow Yellow Gray Yellow Brown Brown
Row 21: Brown Gray Yellow Brown Gray Brown Yellow Gray Yellow Brown Yellow Yellow Yellow Gray Yellow Gray
Example 3
Input:
Row 1: Brown Gray Gray Brown Brown Gray Gray Gray
Row 2: Brown Brown Gray Brown Brown Gray Gray Brown
Row 3: Brown Brown Gray Gray Gray Gray Gray Brown
Row 4: Gray Gray Brown Brown Brown Gray Gray Brown
Row 5: Brown Brown Gray Gray Brown Brown Gray Gray
Row 6: Brown Brown Brown Brown Gray Brown Gray Brown
Row 7: Gray Gray Gray Gray Gray Gray Brown Gray
Row 8: Gray Gray Gray Gray Brown Gray Brown Gray
Row 9: Brown Brown Gray Brown Gray Gray Brown Brown
Row 10: Gray Brown Brown Brown Gray Brown Brown Gray
Row 11: Gray Gray Brown Gray Brown Gray Gray Brown
Row 12: Brown Brown Brown Gray Gray Brown Brown Gray
Row 13: Gray Gray Brown Brown Gray Brown Brown Gray
Row 14: Brown Gray Brown Brown Gray Brown Gray Brown
Row 15: Gray Gray Brown Brown Gray Brown Gray Gray
Row 16: Brown Gray Gray Brown Gray Brown Gray Brown
Row 17: Gray Brown Brown Gray Gray Brown Gray Brown
Row 18: Gray Gray Gray Gray Brown Brown Brown Brown
Row 19: Brown Gray Gray Brown Gray Gray Brown Gray
Row 20: Gray Gray Gray Brown Gray Gray Brown Gray
Output:
Row 1: Purple Blue Blue Purple Purple Blue Blue Blue
Row 2: Purple Purple Blue Purple Purple Blue Blue Purple
Row 3: Purple Purple Blue Blue Blue Blue Blue Purple
Row 4: Blue Blue Purple Purple Purple Blue Blue Purple
Row 5: Purple Purple Blue Blue Purple Purple Blue Blue
Row 6: Purple Purple Purple Purple Blue Purple Blue Purple
Row 7: Blue Blue Blue Blue Blue Blue Purple Blue
Row 8: Blue Blue Blue Blue Purple Blue Purple Blue
Row 9: Purple Purple Blue Purple Blue Blue Purple Purple
Row 10: Blue Purple Purple Purple Blue Purple Purple Blue
Row 11: Blue Blue Purple Blue Purple Blue Blue Purple
Row 12: Purple Purple Purple Blue Blue Purple Purple Blue
Row 13: Blue Blue Purple Purple Blue Purple Purple Blue
Row 14: Purple Blue Purple Purple Blue Purple Blue Purple
Row 15: Blue Blue Purple Purple Blue Purple Blue Blue
Row 16: Purple Blue Blue Purple Blue Purple Blue Purple
Row 17: Blue Purple Purple Blue Blue Purple Blue Purple
Row 18: Blue Blue Blue Blue Purple Purple Purple Purple
Row 19: Purple Blue Blue Purple Blue Blue Purple Blue
Row 20: Blue Blue Blue Purple Blue Blue Purple Blue
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Green Yellow Green Green Yellow Green Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Green Yellow Green Green Green Yellow Yellow Green Yellow Yellow Yellow Green Green Green
Row 3: Green Yellow Green Yellow Yellow Yellow Green Green Green Green Yellow Green Green Green Green
Row 4: Green Yellow Yellow Green Yellow Green Yellow Green Yellow Green Green Green Yellow Yellow Yellow
Row 5: Yellow Yellow Green Green Yellow Yellow Green Yellow Yellow Green Yellow Yellow Green Green Green
Row 6: Green Yellow Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Green
Row 7: Yellow Green Green Yellow Yellow Yellow Green Yellow Green Green Yellow Green Green Green Yellow
Row 8: Green Yellow Green Yellow Green Green Green Yellow Green Yellow Yellow Yellow Green Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green
Row 10: Green Yellow Green Green Green Green Yellow Green Yellow Yellow Green Green Yellow Yellow Green
Row 11: Yellow Green Yellow Green Green Yellow Yellow Green Green Green Yellow Yellow Green Green Green
Row 12: Yellow Green Green Yellow Yellow Yellow Green Green Green Green Yellow Yellow Yellow Green Yellow
Row 13: Green Yellow Yellow Green Green Green Green Yellow Yellow Yellow Green Yellow Green Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Green Green Yellow Yellow Green Yellow Yellow Yellow Green Yellow
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Green Yellow Green Yellow Yellow Green Yellow Yellow Green Green Green Green Green Green
Green Yellow Green Yellow Yellow Yellow Green Green Yellow Green Green Green Yellow Yellow Yellow
Yellow Green Yellow Green Green Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow
Yellow Green Green Yellow Green Yellow Green Yellow Green Yellow Yellow Yellow Green Green Green
Green Green Yellow Yellow Green Green Yellow Green Green Yellow Green Green Yellow Yellow Yellow
Yellow Green Yellow Green Yellow Green Green Green Green Green Green Green Yellow Green Yellow
Green Yellow Yellow Green Green Green Yellow Green Yellow Yellow Green Yellow Yellow Yellow Green
Yellow Green Yellow Green Yellow Yellow Yellow Green Yellow Green Green Green Yellow Green Green
Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Yellow
Yellow Green Yellow Yellow Yellow Yellow Green Yellow Green Green Yellow Yellow Green Green Yellow
Green Yellow Green Yellow Yellow Green Green Yellow Yellow Yellow Green Green Yellow Yellow Yellow
Green Yellow Yellow Green Green Green Yellow Yellow Yellow Yellow Green Green Green Yellow Green
Yellow Green Green Yellow Yellow Yellow Yellow Green Green Green Yellow Green Yellow Green Green
Green Green Green Green Green Yellow Yellow Green Green Yellow Green Green Green Yellow 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: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Pink Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Green Brown Green Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Green Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown
Row 5: Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Pink Pink Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink 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
Row 12: Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Gray Brown Brown Brown Brown
Row 13: 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
Row 14: Brown Brown Brown Brown Pink Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: 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
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Pink Brown Brown Pink Green Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Pink Green Brown Brown Green Brown Green Brown Brown Green Brown Green Brown Brown Gray Green Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Green Brown Green Brown Gray Green Brown Brown Brown Brown Green Gray Brown Brown Green Brown Green Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Green Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Pink Brown Brown
Row 5: Gray Gray Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Gray Gray Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Pink Brown Brown Brown Brown
Row 7: Green Green Brown Brown Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Pink Brown Green Brown Green Brown Brown Brown Brown
Row 8: Green Green Brown Brown Green Green Brown Brown Brown Green Gray Brown Brown Brown Green Brown Green Brown Gray Green Brown Brown Brown Brown Brown
Row 9: Brown Brown Green Green Pink Pink Brown Brown Green Brown Green Brown Brown Brown Gray Green Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Green Green Pink Pink Brown Brown Pink Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Pink 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 Green Brown Brown
Row 12: Brown Brown Gray Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Green Brown Brown Gray Green Brown Brown Brown
Row 13: Brown Brown Green Brown Green Brown Brown Brown Brown Brown Brown Brown Gray Green Brown Brown Green Brown Green Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Green Pink Brown Pink Green Brown Brown Brown Brown Green Brown Green Brown Brown Green Gray Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Green Brown Green Brown Brown Brown Brown Green Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Green Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
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 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 Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange 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 Orange Orange Orange Orange 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 Orange Orange Orange Orange 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 Orange Orange Orange Orange 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 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 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 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 Gray Gray Gray Gray 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 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 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 Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Green Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Green Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Green Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Green 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 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 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 Orange 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 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 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 Green 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 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 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 Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Brown Brown Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Brown Brown Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Brown Brown Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Brown Brown Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown 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 Brown Brown Brown Brown 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 Brown Brown Brown Brown 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 Brown Brown Brown Brown 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 Brown Brown Brown Brown Brown Brown Brown Brown Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray 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 Brown Brown Brown Brown Brown Brown Brown Brown Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Orange Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown Green Green Green Green Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown Green Green Green Green Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown Green Green Green Green Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Brown Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown Green Green Green Green 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 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 Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Orange 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 Brown 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 Brown Brown 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 Green Brown 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 Gray Gray Gray Gray Gray Gray Gray
Example 3
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Orange Green Green Green Orange Green Green Green Green Green Green Green Green Green Green Blue Green
Row 3: Green Green Green Blue Green Green Green Blue Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange Green Green Orange
Row 4: Green Green Orange Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Orange Orange Green Green Green
Row 5: Green Green Green Green Green Green Green Green Blue Green Green Blue Blue Green Green Green Green Green Blue Blue Green Green Green Green Blue
Row 6: Green Green Green Green Green Orange Green Green Green Orange Green Green Green Orange Orange Green Green Green Blue Blue Green Green Green Orange Green
Row 7: Green Green Orange Green Blue Green Green Green Green Green Green Green Green Orange Orange Green Green Green Green Green Green Green Green Green Green
Row 8: Green Blue Green Green Green Green Green Orange 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 Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Green Green Green Green Green Green Green Blue Green Green
Row 11: Green Green Green Green Green Green Blue Blue Green Green Green Blue Blue Blue Blue Green Green Green Green Green Green Green Green Green Green
Row 12: Green Blue Green Green Green Green Blue Blue Green Green Green Blue Blue Blue Blue Green Green Green Green Green Green Green Blue Pink Green
Row 13: Green Green Orange Green Orange Orange Green Green Green Green Green Blue Blue Blue Blue Green Green Green Green Green Green Green Pink Orange Green
Row 14: Green Green Green Green Orange Orange Green Green Green Green Green Green Green Green Green Orange Orange Orange Orange Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange Orange Orange Green Green Green Green Green Green
Row 16: Green Green Green Orange Green Green Green Green Green Green Green Green Green Green Green Orange Orange Orange Orange Green Green Green Green Blue Green
Row 17: Green Green Blue Green Green Green Orange Orange Green Green Green Green Green Green Green Orange Orange Orange Orange Green Green Green Orange Green Green
Row 18: Green Green Green Green Green Green Orange Orange 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 Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange
Row 20: Green Green Blue Green Green Green Green Green Blue Blue Green Green Blue Green Green Green Blue Green Green Green Blue Green Green Blue Green
Row 21: Green Orange Green Green Green Green Green Green Green Green Green Green Green Orange Green Orange Green Green Green Green Green Orange Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Pink Blue Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Pink Orange Green Green Green Orange Pink Green Green Green Green Green Green Green Green Green Blue Pink
Row 3: Green Green Pink Blue Green Green Green Blue Pink Green Green Green Green Green Green Green Green Green Pink Pink Orange Orange Green Pink Orange
Row 4: Green Green Orange Pink Green Green Green Green Green Green Green Blue Blue Pink Pink Green Green Green Pink Pink Orange Orange Green Green Green
Row 5: Green Green Green Green Green Green Green Green Blue Pink Green Blue Blue Pink Pink Green Green Green Blue Blue Pink Pink Green Pink Blue
Row 6: Green Green Green Green Pink Orange Green Green Pink Orange Green Pink Pink Orange Orange Green Green Green Blue Blue Pink Pink Green Orange Pink
Row 7: Green Pink Orange Green Blue Pink Green Green Green Green Green Pink Pink Orange Orange Green Green Green Green Green Green Green Green Green Green
Row 8: Green Blue Pink Green Green Green Green Orange Pink 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 Pink Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Orange Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Pink Pink Pink Pink Green Green Green Blue Pink Green
Row 11: Green Green Green Green Pink Pink Blue Blue Green Green Green Blue Blue Blue Blue Pink Pink Pink Pink Green Green Green Green Green Green
Row 12: Green Blue Pink Green Pink Pink Blue Blue Green Green Green Blue Blue Blue Blue Pink Pink Pink Pink Green Green Green Blue Pink Green
Row 13: Green Pink Orange Green Orange Orange Pink Pink Green Green Green Blue Blue Blue Blue Pink Pink Pink Pink Green Green Green Pink Orange Green
Row 14: Green Green Green Green Orange Orange Pink Pink Green Green Green Pink Pink Pink Pink Orange Orange Orange Orange Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Pink Pink Pink Pink Orange Orange Orange Orange Green Green Green Green Green Green
Row 16: Green Green Pink Orange Green Green Green Green Green Green Green Pink Pink Pink Pink Orange Orange Orange Orange Green Green Green Pink Blue Green
Row 17: Green Green Blue Pink Green Green Orange Orange Pink Pink Green Pink Pink Pink Pink Orange Orange Orange Orange Green Green Green Orange Pink Green
Row 18: Green Green Green Green Green Green Orange Orange Pink Pink Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Pink Pink Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Orange
Row 20: Green Pink Blue Green Green Green Pink Pink Blue Blue Green Green Blue Pink Green Pink Blue Green Green Green Blue Pink Green Blue Pink
Row 21: Green Orange Pink Green Green Green Green Green Green Green Green Green Pink Orange Green Orange Pink Green Green Green Pink Orange Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Gray Gray Gray Gray Gray Gray Gray
Row 2: Pink Pink Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Gray Gray Gray Gray Gray Gray Gray
Row 3: Pink Pink Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Green Green Green Gray Gray Gray Gray Gray Pink Gray
Row 4: Gray Gray Green Green Gray Gray Pink Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Gray Green Gray Gray
Row 5: Gray Gray Green Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Pink Pink Pink Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Pink Pink Pink Gray Green Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray
Row 8: Gray Gray Gray Green Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Pink Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Green Gray Gray Gray Green Gray Gray Black Pink Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Green Gray Gray Gray Pink Gray Gray Pink Gray Pink Gray Gray Gray Green Black Gray
Row 11: Gray Gray Pink Gray Gray Gray Pink Gray Gray Gray Gray Gray Pink Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Green Gray Green Gray Gray Gray Pink 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 Green Gray Gray Gray Green Gray Gray Gray Green Gray Gray Gray Gray Pink Gray Green Gray Gray Gray Gray Pink Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Pink Gray Gray Gray Gray Green Gray Gray Gray Pink Gray 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 Black Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Black Black Black Gray Gray Gray Gray
Pink Pink Black Black Gray Gray Gray Gray Pink Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Black Black Black Gray Gray Gray Gray
Pink Pink Black Black Gray Green Black Gray Gray Gray Gray Gray Black Green Gray Gray Gray Gray Gray Gray Green Green Green Black Black Black Gray Black Pink Gray
Black Black Green Green Gray Black Pink Gray Gray Gray Gray Gray Pink Black Gray Gray Gray Gray Gray Gray Black Black Black Pink Pink Pink Gray Green Black Gray
Black Black Green Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Green Gray Black Black Black Pink Pink Pink Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Black Gray Gray Gray Gray Gray Pink Black Gray Black Black Black Pink Pink Pink Gray Green Black Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Pink Gray Pink Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Pink Gray
Gray Gray Black Green Gray Gray Pink Black Gray Gray Gray Gray Gray Black Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Pink Black Gray Gray Black Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Black Gray Green Black Gray Black Green Gray Gray Black Pink Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Black Gray Green Black Gray Black Pink Gray Black Pink Gray Pink Black Gray Gray Green Black Gray
Gray Gray Pink Black Gray Black Pink Gray Gray Gray Gray Black Pink Gray Black Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Black Green Gray Green Black Gray Black 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 Green Black Gray Black Green Gray Gray Black Green Gray Gray Gray Black Pink Gray Green Black Gray Gray Gray Pink Black
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Black Gray Gray Pink Black Gray Gray Gray Green Black Gray Black Pink Gray Gray Gray Black 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 Gray Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Black Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray
Row 3: Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray
Row 4: Gray Black Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray
Row 5: Gray Black Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray
Row 6: Gray Black Gray Black Gray Black Black Black Black Black Gray Black Gray Gray Gray Black Gray Gray
Row 7: Gray Black Gray Black Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Black Gray Gray
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Gray Gray
Row 9: Gray Black Gray Black Gray Gray Gray Gray Gray Gray Gray Black Gray Black Gray Black Gray Gray
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Gray Black Gray Black Gray Gray Gray Gray Gray Gray Gray Black Gray Black Gray Gray Gray Gray
Row 12: Gray Black Gray Black Gray Gray Gray Gray Black Black Black Black Gray Black Gray Gray Gray Gray
Row 13: Gray Black Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray
Output:
Row 1: Green Green Green Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Black Green Black Green Green Green Green Green Green Green Green Green Green Green Black Green Green
Row 3: Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Black Green Green
Row 4: Green Black Red Black Green Green Green Green Green Green Green Green Green Green Green Black Green Green
Row 5: Green Black Red Black Green Green Green Green Green Green Green Green Green Green Green Black Green Green
Row 6: Green Black Red Black Green Black Black Black Black Black Green Black Green Green Green Black Green Green
Row 7: Green Black Red Black Green Green Green Green Green Green Green Black Green Green Green Black Green Green
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black Green Green
Row 9: Green Black Red Black Red Red Red Red Red Red Red Black Red Black Green Black Green Green
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Green Black Red Black Red Red Red Red Red Red Red Black Red Black Green Green Green Green
Row 12: Green Black Red Black Red Red Red Red Black Black Black Black Red Black Green Green Green Green
Row 13: Green Black Red Black Red Red Red Red Red Red Red Red Red Black Green Green Green Green
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Black Green Green Green Green
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 Orange Orange
Row 2: Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange 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 Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
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
Row 2: Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green
Row 4: Green Green Green Green Green Yellow Red Red Red Red Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Yellow Red Red Red Red Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green
Row 7: Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray
Row 2: Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Orange Gray
Row 3: Gray Orange Gray Gray Orange Orange Orange Orange Orange Gray Gray Gray Orange Gray
Row 4: Gray Orange Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Orange Gray
Row 5: Gray Orange Gray Gray Gray Orange Gray Orange Gray Gray Orange Gray Orange Gray
Row 6: Gray Orange Gray Gray Gray Orange Gray Orange Gray Gray Orange Gray Orange Gray
Row 7: Gray Orange Gray Gray Gray Orange Gray Orange Gray Gray Orange Gray Orange Gray
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Gray Orange Gray Gray Gray Orange Gray Orange Gray Gray Orange Gray Orange Gray
Row 10: Gray Orange Gray Gray Gray Orange Gray Orange Gray Gray Orange Gray Orange Gray
Row 11: Gray Orange Gray Gray Gray Orange Gray Orange Gray Gray Orange Gray Orange Gray
Row 12: Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Orange Gray Gray Gray
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Orange Green
Row 2: Green Green Green Green Green Orange Green Green Green Green Green Green Orange Green
Row 3: Green Orange Green Green Orange Orange Orange Orange Orange Green Green Green Orange Green
Row 4: Green Orange Green Green Green Orange Green Green Green Green Green Green Orange Green
Row 5: Green Orange Green Green Green Orange Green Orange Green Green Orange Green Orange Green
Row 6: Green Orange Green Green Green Orange Green Orange Green Green Orange Green Orange Green
Row 7: Green Orange Green Green Green Orange Green Orange Green Green Orange Green Orange Green
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Green Orange Green Green Green Orange Red Orange Red Red Orange Red Orange Green
Row 10: Green Orange Green Green Green Orange Red Orange Red Red Orange Red Orange Green
Row 11: Green Orange Green Green Green Orange Red Orange Red Red Orange Red Orange Green
Row 12: Green Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green
Row 13: Green Green Green Green Green Green Green Orange Green Green Orange Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Brown Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink
Row 3: Pink Pink Brown Pink Brown Pink Brown Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Brown Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink
Row 6: 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>
| Green Green Brown Green Brown Green Green Green Green Green Green Green Green Green
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green
Green Green Brown Red Brown Red Brown Green Green Green Green Green Green Green
Green Green Brown Brown Brown Brown Brown Green Green Green Green Green Green Green
Green Green Brown Green Green Green Brown 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: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown 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 Brown
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 Brown Brown Pink Blue Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Pink Gray 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 Brown Brown Brown Brown
Row 14: 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
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown 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 Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Gray Gray Brown Brown Pink Pink Brown Brown
Row 9: Brown Brown Brown Gray Gray Brown Brown Pink Pink Brown Brown
Row 10: Brown Brown Brown Brown Brown Pink Blue Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Pink Gray Brown Brown Brown Brown
Row 12: Brown Brown Brown Blue Blue Brown Brown Pink Pink Brown Brown
Row 13: Brown Brown Brown Blue Blue Brown Brown Pink Pink Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 2
Input:
Row 1: Black Black Black Yellow Green 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 Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Red Black Black Black Black Blue Blue Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Blue Black Black Black Black Brown 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
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
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
Row 7: Black Black Black Pink Pink Black Black 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 Yellow Orange Black Black Black Black Black Black Black Orange Orange 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 Orange Red Black Black Black Black Black Black Black Black Black Brown Yellow 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 Yellow Pink 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 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 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
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Green Black Black Black Black Black Black Black Black Black Black Red Brown
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Red Blue Black Black Black Black Black Black Black Black Black Black Brown Blue
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: Black Black Black 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 Yellow Green Black Black Black Black Black Black Black Black Black Black Black Blue Blue Black Black Orange Orange Brown Brown Black Black Brown
Row 2: Black Black Black Pink Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Red Black Black Black Black Blue Blue Black
Row 3: Black Green Green Black Black Yellow Yellow Black Black Black Black Black Black Black Black Black Black Black Orange Blue Black Black Black Black Brown Brown Black
Row 4: Black Green Green Black Black Yellow Yellow Black Black Black Black Black Black Black Black Black Red Red Black Black Pink Pink Blue Blue Black Black Blue
Row 5: Black Orange Orange Black Black Yellow Yellow Black Black Black Black Black Black Black Black Black Red Red Black Black Pink Pink Blue Blue Black Black Blue
Row 6: Black Orange Orange Black Black Yellow Yellow Black Black Black Red Red Black Black Orange Orange Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Pink Pink Black Black Black Black Black Red Red Black Black Orange Orange Black Black Black Black Black Pink Pink Black Black Yellow Yellow
Row 8: Black Black Black Yellow Orange Black Black Black Black Black Black Black Orange Orange Black Black Black Black Black Black Black Pink Pink Black Black Yellow Yellow
Row 9: Black Pink Pink Black Black Pink Pink Black Black Black Black Black Orange Red Black Black Black Black Black Black Black Black Black Brown Yellow Black Black
Row 10: Black Pink Pink Black Black Pink Pink Black Black Black Orange Orange Black Black Orange Orange Black Black Black Black Black Black Black Yellow Pink Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Orange Orange Black Black Orange Orange Black Black Black Black Black Yellow Yellow Black Black Brown Brown
Row 12: Black Black Black Black Black Black Black Black Black Black Black Blue Blue Black Black Red Red Black Black Black Black Yellow Yellow Blue Blue Brown Brown
Row 13: Black Black Black Black Black Black Black Black Black Black Black Blue Blue Black Black Red Red Black Black Black Black Black Black Blue Blue Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Green Black Black Black Black Black Black Black Black Black Black Red Brown
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Red Blue Black Black Black Black Black Black Black Black Black Black Brown Blue
Row 16: Black Black Black Black Black Black Black Black Black Black Black Green Green Black Black Orange Orange Black Black Black Black Black Black Brown Brown Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Green Green Black Black Orange Orange Black Black Black Black Black Black Brown Brown Black Black
Example 3
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: Pink Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Blue Pink 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 Pink Purple Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray 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 Gray Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Yellow Purple Brown Brown Brown Brown Brown Brown Brown Purple Green Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Green 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 Purple Pink Brown Brown Brown Brown Brown Brown Brown Purple Blue Brown
Row 20: Brown Brown Brown Purple Pink Brown Brown Brown Brown Brown Brown Brown Green Yellow 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 Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Gray Blue Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Purple Green 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 Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Pink Gray Brown Brown Brown Brown Brown Brown Gray Gray Brown Brown Gray Gray Brown
Row 5: Blue Pink Brown Brown Brown Brown Brown Brown Gray Gray Brown Brown Gray Gray Brown
Row 6: Brown Brown Pink Pink Brown Brown Brown Brown Brown Brown Pink Purple Brown Brown Brown
Row 7: Brown Brown Pink Pink Brown Brown Brown Brown Brown Brown Gray Gray Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Pink Pink Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Pink Pink Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Purple Brown Brown Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Purple Brown Brown Yellow Yellow Brown Brown Brown Green Green Brown Brown Gray Gray Brown
Row 13: Brown Gray Blue Brown Brown Brown Brown Brown Green Green Brown Brown Gray Gray Brown
Row 14: Brown Yellow Purple Brown Brown Brown Brown Brown Brown Brown Purple Green Brown Brown Brown
Row 15: Blue Brown Brown Gray Gray Brown Brown Brown Brown Brown Gray Green Brown Brown Brown
Row 16: Blue Brown Brown Gray Gray Brown Brown Brown Green Green Brown Brown Purple Purple Brown
Row 17: Brown Pink Pink Brown Brown Purple Purple Brown Green Green Yellow Yellow Purple Purple Green
Row 18: Brown Pink Pink Brown Brown Purple Purple Brown Brown Brown Yellow Yellow Brown Brown Green
Row 19: Brown Brown Brown Purple Pink Brown Brown Brown Brown Brown Brown Brown Purple Blue Brown
Row 20: Brown Brown Brown Purple Pink Brown Brown Brown Brown Brown Brown Brown Green Yellow Brown
Row 21: Brown Pink Pink Brown Brown Purple Purple Brown Brown Brown Blue Blue Brown Brown Purple
Row 22: Brown Pink Pink Green Green Purple Purple Purple Purple Brown Blue Blue Brown Brown Purple
Row 23: Brown Brown Brown Green Green Brown Brown Purple Purple Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Gray Blue Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Purple Green Brown Brown Brown Brown Brown Brown Brown Brown
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
Row 2: 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
Row 4: Brown Brown Brown Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Yellow Orange 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
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: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Brown Brown
Row 11: 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
Row 13: Brown Brown Brown Brown Brown Brown Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Orange Yellow 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
Row 18: 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 Yellow Yellow Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Orange 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
Row 22: 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 Orange Orange Brown Brown Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Orange Orange Brown Brown Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Yellow Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Orange Orange Brown Brown Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Orange Orange Brown Brown Orange Orange Brown Brown Brown Brown Brown Brown Brown Orange Orange Brown Brown Orange Orange
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Brown Brown Orange Orange
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Brown Brown
Brown Brown Brown Brown Yellow Yellow Brown Brown Orange Orange Brown Brown Brown Brown Yellow Yellow Brown Brown Yellow Yellow
Brown Brown Brown Brown Yellow Yellow Brown Brown Orange Orange Brown Brown Brown Brown Yellow Yellow Brown Brown Yellow Yellow
Brown Brown Brown Brown Brown Brown Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Orange Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Orange Orange Brown Brown Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Orange Orange Brown Brown Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Brown Brown Yellow Yellow Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Brown Brown Yellow Yellow Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Orange Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Brown Brown Yellow Yellow Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Brown Brown Yellow Yellow 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: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Red Red
Row 12: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Red Red
Row 13: Black Black Brown Brown Brown Brown Brown Brown Red Red Brown Brown
Row 14: Black Black Brown Brown Brown Brown Brown Brown Red Red Brown Brown
Row 15: Black Black Brown Brown Brown Brown Red Red Brown Brown Brown Brown
Row 16: Black Black Brown Brown Brown Brown Red Red Brown Brown Brown Brown
Row 17: Black Black Brown Brown Red Red Brown Brown Brown Brown Brown Brown
Row 18: Black Black Brown Brown Red Red Brown Brown Brown Brown Brown Brown
Row 19: Black Black Red Red Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Black Black Red Red Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Black Black 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
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: 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
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 Purple
Row 8: 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
Row 10: 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
Row 12: 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
Row 14: 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
Row 16: 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
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
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: Yellow Yellow Red Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Yellow Yellow Red Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Yellow Yellow Purple Purple Red Red Purple Purple Purple Purple Purple Purple
Row 6: Yellow Yellow Purple Purple Red Red Purple Purple Purple Purple Purple Purple
Row 7: Yellow Yellow Purple Purple Purple Purple Red Red Purple Purple Purple Purple
Row 8: Yellow Yellow Purple Purple Purple Purple Red Red Purple Purple Purple Purple
Row 9: Yellow Yellow Purple Purple Purple Purple Purple Purple Red Red Purple Purple
Row 10: Yellow Yellow Purple Purple Purple Purple Purple Purple Red Red Purple Purple
Row 11: Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Red Red
Row 12: Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Red Red
Row 13: Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 24: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 25: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red
Row 7: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red
Row 8: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red
Row 9: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red
Row 10: Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red
Row 11: Black Black Black Black Black Pink Pink Pink Pink Pink Red Red Red Red Red Pink Pink Pink Pink Pink
Row 12: Black Black Black Black Black Pink Pink Pink Pink Pink Red Red Red Red Red Pink Pink Pink Pink Pink
Row 13: Black Black Black Black Black Pink Pink Pink Pink Pink Red Red Red Red Red Pink Pink Pink Pink Pink
Row 14: Black Black Black Black Black Pink Pink Pink Pink Pink Red Red Red Red Red Pink Pink Pink Pink Pink
Row 15: Black Black Black Black Black Pink Pink Pink Pink Pink Red Red Red Red Red Pink Pink Pink Pink Pink
Row 16: Black Black Black Black Black Red Red Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Black Black Black Black Black Red Red Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Black Black Black Black Black Red Red Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Black Black Black Black Black Red Red Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Black Black Black Black Black Red Red Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 25: Black Black Black Black 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: Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: 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>
| Pink Pink Pink Pink Pink Pink Pink Pink
Yellow Red Purple Purple Purple Purple Purple Purple
Yellow Purple Red Purple Purple Purple Purple Purple
Yellow Purple Purple Red Purple Purple Purple Purple
Yellow Purple Purple Purple Red Purple Purple Purple
Yellow Purple Purple Purple Purple Red Purple Purple
Yellow Purple Purple Purple Purple Purple Red Purple
Yellow Purple Purple Purple Purple Purple Purple Red
Yellow Purple Purple Purple Purple Purple Purple Purple
Yellow Purple Purple Purple Purple Purple Purple Purple
Yellow Purple Purple Purple Purple Purple Purple Purple
Yellow Purple Purple Purple Purple Purple Purple Purple |
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