

'''simple docstring'''





from __future__ import annotations

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







@dataclass
class 				lowercase       :
				__SCREAMING_SNAKE_CASE      :				int
				__SCREAMING_SNAKE_CASE      :				Node | None     =    None
				__SCREAMING_SNAKE_CASE      :				Node | None     =    None





def       __lowerCamelCase			(				):







							'''simple docstring'''






							snake_case_           =					Node(1   )
							snake_case_           =					Node(2   )
							snake_case_           =					Node(3   )
							snake_case_           =					Node(4   )
							snake_case_           =					Node(5   )
							return tree





def       __lowerCamelCase			(				UpperCamelCase__   ):







							'''simple docstring'''






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





def       __lowerCamelCase			(				UpperCamelCase__   ):







							'''simple docstring'''






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





def       __lowerCamelCase			(				UpperCamelCase__   ):







							'''simple docstring'''






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





def       __lowerCamelCase			(				UpperCamelCase__   ):







							'''simple docstring'''






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





def       __lowerCamelCase			(				UpperCamelCase__   ):







							'''simple docstring'''






							snake_case_           =					[]

							if root is None:
														return output

							snake_case_           =					deque([root]   )

							while process_queue:
														snake_case_           =					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			(				UpperCamelCase__     ,							UpperCamelCase__   ):







							'''simple docstring'''






							snake_case_           =					[]

							def populate_output(UpperCamelCase__     ,							UpperCamelCase__   ) -> 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(UpperCamelCase__     ,							UpperCamelCase__   )
							return output





def       __lowerCamelCase			(				UpperCamelCase__     ,							UpperCamelCase__   ):







							'''simple docstring'''






							snake_case_           =					[]

							def populate_output(UpperCamelCase__     ,							UpperCamelCase__   ) -> 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(UpperCamelCase__     ,							UpperCamelCase__   )
							return output





def       __lowerCamelCase			(				UpperCamelCase__   ):







							'''simple docstring'''






							if root is None:
														return []

							snake_case_           =					[]

							snake_case_           =					0
							snake_case_           =					height(UpperCamelCase__   )

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

							return output





def       __lowerCamelCase			(				):  # Main function for testing.







							'''simple docstring'''






							snake_case_           =					make_tree()
							print(F'''In-order Traversal: {inorder(UpperCamelCase__   )}'''   )
							print(F'''Pre-order Traversal: {preorder(UpperCamelCase__   )}'''   )
							print(F'''Post-order Traversal: {postorder(UpperCamelCase__   )}'''     ,							'\n'   )

							print(F'''Height of Tree: {height(UpperCamelCase__   )}'''     ,							'\n'   )

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

							print('Level-wise order Traversal: '   )

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

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


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					main()







_UpperCAmelCase	:     str		       = [0, 2, 4, 6, 8]
_UpperCAmelCase	:     Any		       = [1, 3, 5, 7, 9]





def       __lowerCamelCase			(				UpperCamelCase__     ,							UpperCamelCase__     ,							UpperCamelCase__     ,							UpperCamelCase__   ):







							'''simple docstring'''






							if remaining_length == 0:
														if digits[0] == 0 or digits[-1] == 0:
																					return 0

														for i in range(length // 2 - 1     ,							-1     ,							-1   ):
																					remainder += digits[i] + digits[length - i - 1]

																					if remainder % 2 == 0:
																												return 0

																					remainder //= 10

														return 1

							if remaining_length == 1:
														if remainder % 2 == 0:
																					return 0

														snake_case_           =					0
														for digit in range(10   ):
																					snake_case_           =					digit
																					result += reversible_numbers(
																					    0     ,							(remainder + 2 * digit) // 10     ,							UpperCamelCase__     ,							UpperCamelCase__   )
														return result

							snake_case_           =					0
							for digita in range(10   ):
														snake_case_           =					digita

														if (remainder + digita) % 2 == 0:
																					snake_case_           =					ODD_DIGITS
														else:
																					snake_case_           =					EVEN_DIGITS

														for digita in other_parity_digits:
																					snake_case_           =					digita
																					result += reversible_numbers(
																					    remaining_length - 2     ,							(remainder + digita + digita) // 10     ,							UpperCamelCase__     ,							UpperCamelCase__     ,							)
							return result





def       __lowerCamelCase			(				UpperCamelCase__ = 9   ):







							'''simple docstring'''






							snake_case_           =					0
							for length in range(1     ,							max_power + 1   ):
														result += reversible_numbers(UpperCamelCase__     ,							0     ,							[0] * length     ,							UpperCamelCase__   )
							return result


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




