






from __future__ import annotations

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



      """simple docstring"""


      a    :					int
      a    :					Node | None							=      None
      a    :					Node | None							=      None






def 							lowerCamelCase__ (       ):
  __UpperCAmelCase				:      Tuple	 =    Node(1						)
  __UpperCAmelCase				:      int	 =    Node(2						)
  __UpperCAmelCase				:      Optional[Any]	 =    Node(3						)
  __UpperCAmelCase				:      Dict	 =    Node(4						)
  __UpperCAmelCase				:      Tuple	 =    Node(5						)
  return tree






def 							lowerCamelCase__ (       __lowerCamelCase     :	Node | None						):
  return [root.data, *preorder(root.left						), *preorder(root.right						)] if root else []






def 							lowerCamelCase__ (       __lowerCamelCase     :	Node | None						):
  return postorder(root.left						) + postorder(root.right						) + [root.data] if root else []






def 							lowerCamelCase__ (       __lowerCamelCase     :	Node | None						):
  return [*inorder(root.left						), root.data, *inorder(root.right						)] if root else []






def 							lowerCamelCase__ (       __lowerCamelCase     :	Node | None						):
  return (max(height(root.left						)    ,						height(root.right						)						) + 1) if root else 0






def 							lowerCamelCase__ (       __lowerCamelCase     :	Node | None						):
  __UpperCAmelCase				:      list[Any]	 =    []

  if root is None:
    return output

  __UpperCAmelCase				:      Tuple	 =    deque([root]						)

  while process_queue:
    __UpperCAmelCase				:      Optional[Any]	 =    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 							lowerCamelCase__ (       __lowerCamelCase     :	Node | None    ,						__lowerCamelCase     :	int						):
  __UpperCAmelCase				:      list[Any]	 =    []

  def populate_output(__lowerCamelCase     :	Node | None    ,						__lowerCamelCase     :	int						) -> 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(__lowerCamelCase    ,						__lowerCamelCase						)
  return output






def 							lowerCamelCase__ (       __lowerCamelCase     :	Node | None    ,						__lowerCamelCase     :	int						):
  __UpperCAmelCase				:      list[Any]	 =    []

  def populate_output(__lowerCamelCase     :	Node | None    ,						__lowerCamelCase     :	int						) -> 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(__lowerCamelCase    ,						__lowerCamelCase						)
  return output






def 							lowerCamelCase__ (       __lowerCamelCase     :	Node | None						):
  if root is None:
    return []

  __UpperCAmelCase				:      list[Sequence[Node | None]]	 =    []

  __UpperCAmelCase				:      Optional[int]	 =    0
  __UpperCAmelCase				:      int	 =    height(__lowerCamelCase						)

  for h in range(1    ,						height_tree + 1						):
    if not flag:
      output.append(get_nodes_from_left_to_right(__lowerCamelCase    ,						__lowerCamelCase						)						)
      __UpperCAmelCase				:      List[Any]	 =    1
    else:
      output.append(get_nodes_from_right_to_left(__lowerCamelCase    ,						__lowerCamelCase						)						)
      __UpperCAmelCase				:      Optional[int]	 =    0

  return output






def 							lowerCamelCase__ (       ):  # Main function for testing.
  __UpperCAmelCase				:      List[Any]	 =    make_tree()
  print(f"""In-order Traversal: {inorder(__lowerCamelCase						)}"""						)
  print(f"""Pre-order Traversal: {preorder(__lowerCamelCase						)}"""						)
  print(f"""Post-order Traversal: {postorder(__lowerCamelCase						)}"""    ,						"""\n"""						)

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

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

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

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

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


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       main()










'''simple docstring'''
from __future__ import annotations




def 		__SCREAMING_SNAKE_CASE       (	_UpperCamelCase				):


   """simple docstring"""




   lowercase_						:     Optional[int]							     =  2
   lowercase_						:     Tuple							     =  []
   while i * i <= n:
      if n % i:
         i += 1
      else:
         n //= i
         factors.append(_UpperCamelCase				)
   if n > 1:
      factors.append(_UpperCamelCase				)
   return factors


if __name__ == "__main__":
 import doctest

 doctest.testmod()




