from __future__ import annotations

from collections import deque
from collections.abc import Sequence
from dataclasses import dataclass
from typing import Any





@dataclass
class UpperCAmelCase						:


				'''simple docstring'''






				lowerCamelCase_    = 42
				lowerCamelCase_    = None
				lowerCamelCase_    = None




def     UpperCamelCase						(	):
		'''simple docstring'''




		A_		:    List[Any]         =				Node(1     )
		A_		:    str         =				Node(2     )
		A_		:    List[str]         =				Node(3     )
		A_		:    List[Any]         =				Node(4     )
		A_		:    List[str]         =				Node(5     )
		return tree




def     UpperCamelCase						(	__lowercase						:			Node | None     ):
		'''simple docstring'''




		return [root.data, *preorder(root.left     ), *preorder(root.right     )] if root else []




def     UpperCamelCase						(	__lowercase						:			Node | None     ):
		'''simple docstring'''




		return postorder(root.left     ) + postorder(root.right     ) + [root.data] if root else []




def     UpperCamelCase						(	__lowercase						:			Node | None     ):
		'''simple docstring'''




		return [*inorder(root.left     ), root.data, *inorder(root.right     )] if root else []




def     UpperCamelCase						(	__lowercase						:			Node | None     ):
		'''simple docstring'''




		return (max(height(root.left     )						,height(root.right     )     ) + 1) if root else 0




def     UpperCamelCase						(	__lowercase						:			Node | None     ):
		'''simple docstring'''




		A_		:    list[Any]         =				[]

		if root is None:
				return output

		A_		:    Optional[Any]         =				deque([root]     )

		while process_queue:
				A_		:    List[str]         =				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     UpperCamelCase						(	__lowercase						:			Node | None						,__lowercase						:			int     ):
		'''simple docstring'''




		A_		:    list[Any]         =				[]

		def populate_output(__lowercase						:			Node | None						,__lowercase						:			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(__lowercase						,__lowercase     )
		return output




def     UpperCamelCase						(	__lowercase						:			Node | None						,__lowercase						:			int     ):
		'''simple docstring'''




		A_		:    list[Any]         =				[]

		def populate_output(__lowercase						:			Node | None						,__lowercase						:			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(__lowercase						,__lowercase     )
		return output




def     UpperCamelCase						(	__lowercase						:			Node | None     ):
		'''simple docstring'''




		if root is None:
				return []

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

		A_		:    Optional[Any]         =				0
		A_		:    List[str]         =				height(__lowercase     )

		for h in range(1						,height_tree + 1     ):
				if not flag:
						output.append(get_nodes_from_left_to_right(__lowercase						,__lowercase     )     )
						A_		:    Dict         =				1
				else:
						output.append(get_nodes_from_right_to_left(__lowercase						,__lowercase     )     )
						A_		:    str         =				0

		return output




def     UpperCamelCase						(	):  # Main function for testing.
		'''simple docstring'''




		A_		:    Union[str, Any]         =				make_tree()
		print(f'''In-order Traversal: {inorder(__lowercase     )}'''     )
		print(f'''Pre-order Traversal: {preorder(__lowercase     )}'''     )
		print(f'''Post-order Traversal: {postorder(__lowercase     )}'''						,'\n'     )

		print(f'''Height of Tree: {height(__lowercase     )}'''						,'\n'     )

		print('Complete Level Order Traversal: '     )
		print(level_order(__lowercase     )						,'\n'     )

		print('Level-wise order Traversal: '     )

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

		print('\nZigZag order Traversal: '     )
		print(zigzag(__lowercase     )     )


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()







import math




def     UpperCamelCase						(	__lowercase						:			int = 1_00     ):
		'''simple docstring'''




		A_		:    List[Any]         =				sum(i * i for i in range(1						,n + 1     )     )
		A_		:    int         =				int(math.pow(sum(range(1						,n + 1     )     )						,2     )     )
		return square_of_sum - sum_of_squares


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






