






from __future__ import annotations

from collections import deque
from collections.abc import Sequence
from dataclasses import dataclass
from typing import Any
@dataclass
class 		SCREAMING_SNAKE_CASE__	:

  '''simple docstring'''







  _lowerCamelCase    =  42
  _lowerCamelCase    =  None
  _lowerCamelCase    =  None




def       _SCREAMING_SNAKE_CASE (							)				->						Node | None:
       _UpperCAmelCase							=    Node(1 )
       _UpperCAmelCase							=    Node(2 )
       _UpperCAmelCase							=    Node(3 )
       _UpperCAmelCase							=    Node(4 )
       _UpperCAmelCase							=    Node(5 )
       return tree




def       _SCREAMING_SNAKE_CASE (							__snake_case )				->						list[int]:
       return [root.data, *preorder(root.left ), *preorder(root.right )] if root else []




def       _SCREAMING_SNAKE_CASE (							__snake_case )				->						list[int]:
       return postorder(root.left ) + postorder(root.right ) + [root.data] if root else []




def       _SCREAMING_SNAKE_CASE (							__snake_case )				->						list[int]:
       return [*inorder(root.left ), root.data, *inorder(root.right )] if root else []




def       _SCREAMING_SNAKE_CASE (							__snake_case )				->						int:
       return (max(height(root.left )   ,      height(root.right ) ) + 1) if root else 0




def       _SCREAMING_SNAKE_CASE (							__snake_case )				->						Sequence[Node | None]:
       _UpperCAmelCase							=    []

       if root is None:
              return output

       _UpperCAmelCase							=    deque([root] )

       while process_queue:
              _UpperCAmelCase							=    process_queue.popleft()
              output.append(node.data )

              if node.left:
                     process_queue.append(node.left )
              if node.right:
                     process_queue.append(node.right )
       return output




def       _SCREAMING_SNAKE_CASE (							__snake_case   ,      __snake_case )				->						Sequence[Node | None]:
       _UpperCAmelCase							=    []

       def populate_output(__snake_case   ,      __snake_case ) -> None:
              if not root:
                     return
              if level == 1:
                     output.append(root.data )
              elif level > 1:
                     populate_output(root.left   ,      level - 1 )
                     populate_output(root.right   ,      level - 1 )

       populate_output(__snake_case   ,      __snake_case )
       return output




def       _SCREAMING_SNAKE_CASE (							__snake_case   ,      __snake_case )				->						Sequence[Node | None]:
       _UpperCAmelCase							=    []

       def populate_output(__snake_case   ,      __snake_case ) -> None:
              if root is None:
                     return
              if level == 1:
                     output.append(root.data )
              elif level > 1:
                     populate_output(root.right   ,      level - 1 )
                     populate_output(root.left   ,      level - 1 )

       populate_output(__snake_case   ,      __snake_case )
       return output




def       _SCREAMING_SNAKE_CASE (							__snake_case )				->						Sequence[Node | None] | list[Any]:
       if root is None:
              return []

       _UpperCAmelCase							=    []

       _UpperCAmelCase							=    0
       _UpperCAmelCase							=    height(__snake_case )

       for h in range(1   ,      height_tree + 1 ):
              if not flag:
                     output.append(get_nodes_from_left_to_right(__snake_case   ,      __snake_case ) )
                     _UpperCAmelCase							=    1
              else:
                     output.append(get_nodes_from_right_to_left(__snake_case   ,      __snake_case ) )
                     _UpperCAmelCase							=    0

       return output




def       _SCREAMING_SNAKE_CASE (							)				->						None:  # Main function for testing.
       _UpperCAmelCase							=    make_tree()
       print(f"""In-order Traversal: {inorder(__snake_case )}""" )
       print(f"""Pre-order Traversal: {preorder(__snake_case )}""" )
       print(f"""Post-order Traversal: {postorder(__snake_case )}"""   ,      """\n""" )

       print(f"""Height of Tree: {height(__snake_case )}"""   ,      """\n""" )

       print("""Complete Level Order Traversal: """ )
       print(level_order(__snake_case )   ,      """\n""" )

       print("""Level-wise order Traversal: """ )

       for level in range(1   ,      height(__snake_case ) + 1 ):
              print(f"""Level {level}:"""   ,      get_nodes_from_left_to_right(__snake_case   ,      level=__snake_case ) )

       print("""\nZigZag order Traversal: """ )
       print(zigzag(__snake_case ) )


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()







def       _SCREAMING_SNAKE_CASE (							__snake_case = 1_0_0_0 )				->						int:
       _UpperCAmelCase	,			_UpperCAmelCase							=    1, 1
       _UpperCAmelCase							=    []
       for i in range(1   ,      n + 1 ):
              _UpperCAmelCase							=    prev_numerator + 2 * prev_denominator
              _UpperCAmelCase							=    prev_numerator + prev_denominator
              if len(str(__snake_case ) ) > len(str(__snake_case ) ):
                     result.append(__snake_case )
              _UpperCAmelCase							=    numerator
              _UpperCAmelCase							=    denominator

       return len(__snake_case )


if __name__ == "__main__":
  print(F"{solution() = }")