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def add_binary_tree_nodes(node, current_depth=0):
            """
            Add binary tree nodes recursively with proper styling.
            """
            if not node:
                return
            
            node_id = node.get('id', f'node_{current_depth}')
            node_label = node.get('label', 'Node')
            
            # Calculate color for current depth using the same logic as graph_generator_utils
            lightening_factor = 0.12 
            
            # Convert base_color hex to RGB for interpolation
            if not isinstance(base_color, str) or not base_color.startswith('#') or len(base_color) != 7:
                base_color_safe = '#19191a'  # Fallback to default dark if invalid
            else:
                base_color_safe = base_color
                
            base_r = int(base_color_safe[1:3], 16)
            base_g = int(base_color_safe[3:5], 16)
            base_b = int(base_color_safe[5:7], 16)
            
            # Calculate current node color by blending towards white
            current_r = base_r + int((255 - base_r) * current_depth * lightening_factor)
            current_g = base_g + int((255 - base_g) * current_depth * lightening_factor)
            current_b = base_b + int((255 - base_b) * current_depth * lightening_factor)
            
            # Clamp values to 255 to stay within valid RGB range
            current_r = min(255, current_r)
            current_g = min(255, current_g)
            current_b = min(255, current_b)
            
            node_color = f'#{current_r:02x}{current_g:02x}{current_b:02x}'
            
            # Font color: white for dark nodes, black for very light nodes for readability
            font_color = 'white' if current_depth * lightening_factor < 0.6 else 'black'
            
            # Font size adjusts based on depth, ensuring a minimum size
            font_size = max(9, 14 - (current_depth * 2))
            
            # Add the current node
            dot.node(
                node_id,
                node_label,
                shape='circle',
                style='filled',
                fillcolor=node_color,
                fontcolor=font_color,
                fontsize=str(font_size),
                width='0.8',
                height='0.8'
            )
            
            # Edge color
            edge_color = '#4a4a4a'  # Dark gray for lines
            
            # Process left child
            left_child = node.get('left')
            if left_child:
                add_binary_tree_nodes(left_child, current_depth + 1)
                left_id = left_child.get('id', f'node_{current_depth + 1}_left')
                dot.edge(
                    node_id,
                    left_id,
                    color=edge_color,
                    arrowsize='0.8'
                )
            
            # Process right child
            right_child = node.get('right')
            if right_child:
                add_binary_tree_nodes(right_child, current_depth + 1)
                right_id = right_child.get('id', f'node_{current_depth + 1}_right')
                dot.edge(
                    node_id,
                    right_id,
                    color=edge_import graphviz
import json
from tempfile import NamedTemporaryFile
import os

def generate_binary_tree_diagram(json_input: str, output_format: str) -> str:
    """
    Generates a binary tree diagram from JSON input.

    Args:
        json_input (str): A JSON string describing the binary tree structure.
                          It must follow the Expected JSON Format Example below.

    Expected JSON Format Example:
    {
      "root": {
        "id": "root",
        "label": "50",
        "left": {
          "id": "left_1",
          "label": "30",
          "left": {
            "id": "left_2",
            "label": "20"
          },
          "right": {
            "id": "right_2",
            "label": "40"
          }
        },
        "right": {
          "id": "right_1",
          "label": "70",
          "left": {
            "id": "left_3",
            "label": "60"
          },
          "right": {
            "id": "right_3",
            "label": "80"
          }
        }
      }
    }

    Returns:
        str: The filepath to the generated PNG image file.
    """
    try:
        if not json_input.strip():
            return "Error: Empty input"
            
        data = json.loads(json_input)
        
        if 'root' not in data:
            raise ValueError("Missing required field: root")

        dot = graphviz.Digraph(
            name='BinaryTree',
            format='png',
            graph_attr={
                'rankdir': 'TB',        # Top-to-Bottom layout (vertical hierarchy)
                'splines': 'line',      # Straight lines
                'bgcolor': 'white',     # White background
                'pad': '0.5',           # Padding around the graph
                'nodesep': '0.8',       # Spacing between nodes
                'ranksep': '1.0'        # Spacing between levels
            }
        )
        
        base_color = '#19191a' # Hardcoded base color
        
        def add_binary_tree_nodes(node, current_depth=0):
            """
            Add binary tree nodes recursively with proper styling.
            """
            if not node:
                return
            
            node_id = node.get('id', f'node_{current_depth}')
            node_label = node.get('label', 'Node')
            
            # Calculate color for current depth using same logic as graph_generator_utils
            lightening_factor = 0.12 
            
            # Convert base_color hex to RGB for interpolation
            if not isinstance(base_color, str) or not base_color.startswith('#') or len(base_color) != 7:
                base_color_safe = '#19191a'  # Fallback to default dark if invalid
            else:
                base_color_safe = base_color
                
            base_r = int(base_color_safe[1:3], 16)
            base_g = int(base_color_safe[3:5], 16)
            base_b = int(base_color_safe[5:7], 16)
            
            # Calculate current node color by blending towards white
            current_r = base_r + int((255 - base_r) * current_depth * lightening_factor)
            current_g = base_g + int((255 - base_g) * current_depth * lightening_factor)
            current_b = base_b + int((255 - base_b) * current_depth * lightening_factor)
            
            # Clamp values to 255 to stay within valid RGB range
            current_r = min(255, current_r)
            current_g = min(255, current_g)
            current_b = min(255, current_b)
            
            node_color = f'#{current_r:02x}{current_g:02x}{current_b:02x}'
            
            # Font color: white for dark nodes, black for very light nodes for readability
            font_color = 'white' if current_depth * lightening_factor < 0.6 else 'black'
            
            # Font size adjusts based on depth, ensuring a minimum size
            font_size = max(9, 14 - (current_depth * 2))
            
            # Add the current node
            dot.node(
                node_id,
                node_label,
                shape='circle',
                style='filled',
                fillcolor=node_color,
                fontcolor=font_color,
                fontsize=str(font_size),
                width='0.8',
                height='0.8'
            )
            
            # Process left child
            left_child = node.get('left')
            if left_child:
                add_binary_tree_nodes(left_child, current_depth + 1)
                left_id = left_child.get('id', f'node_{current_depth + 1}_left')
                dot.edge(
                    node_id,
                    left_id,
                    color='#4a4a4a',  # Dark gray for lines
                    arrowsize='0.8'
                )
            
            # Process right child
            right_child = node.get('right')
            if right_child:
                add_binary_tree_nodes(right_child, current_depth + 1)
                right_id = right_child.get('id', f'node_{current_depth + 1}_right')
                dot.edge(
                    node_id,
                    right_id,
                    color='#4a4a4a',  # Dark gray for lines
                    arrowsize='0.8'
                )
        
        # Add binary tree nodes and edges recursively
        add_binary_tree_nodes(data['root'], current_depth=0)

        with NamedTemporaryFile(delete=False, suffix=f'.{output_format}') as tmp:
            dot.render(tmp.name, format=output_format, cleanup=True)
            return f"{tmp.name}.{output_format}"

    except json.JSONDecodeError:
        return "Error: Invalid JSON format"
    except Exception as e:
        return f"Error: {str(e)}"