"""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       a_      :
					UpperCamelCase_ :	Tuple			=    42
					UpperCamelCase_ :	Union[str, Any]			=    None
					UpperCamelCase_ :	Tuple			=    None







def 							_UpperCAmelCase		(       ):





		"""simple docstring"""




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







def 							_UpperCAmelCase		(       lowerCamelCase__     ):





		"""simple docstring"""




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







def 							_UpperCAmelCase		(       lowerCamelCase__     ):





		"""simple docstring"""




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







def 							_UpperCAmelCase		(       lowerCamelCase__     ):





		"""simple docstring"""




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







def 							_UpperCAmelCase		(       lowerCamelCase__     ):





		"""simple docstring"""




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







def 							_UpperCAmelCase		(       lowerCamelCase__     ):





		"""simple docstring"""




		lowerCAmelCase__        =   []

		if root is None:
				return output

		lowerCAmelCase__        =   deque([root]     )

		while process_queue:
				lowerCAmelCase__        =   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		(       lowerCamelCase__			,  lowerCamelCase__     ):





		"""simple docstring"""




		lowerCAmelCase__        =   []

		def populate_output(lowerCamelCase__			,  lowerCamelCase__     ) -> 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 							_UpperCAmelCase		(       lowerCamelCase__			,  lowerCamelCase__     ):





		"""simple docstring"""




		lowerCAmelCase__        =   []

		def populate_output(lowerCamelCase__			,  lowerCamelCase__     ) -> 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 							_UpperCAmelCase		(       lowerCamelCase__     ):





		"""simple docstring"""




		if root is None:
				return []

		lowerCAmelCase__        =   []

		lowerCAmelCase__        =   0
		lowerCAmelCase__        =   height(_UpperCamelCase     )

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

		return output







def 							_UpperCAmelCase		(       ):  # Main function for testing.





		"""simple docstring"""




		lowerCAmelCase__        =   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()




"""simple docstring"""




def 							_UpperCAmelCase		(       lowerCamelCase__     ):





		"""simple docstring"""




		assert isinstance(lowerCamelCase__			,  lowerCamelCase__     ), f"""The input value of [n={number}] is not an integer"""

		if number == 1:
				return 2
		elif number < 1:
				lowerCAmelCase__        =   f"""The input value of [n={number}] has to be > 0"""
				raise ValueError(lowerCamelCase__     )
		else:
				lowerCAmelCase__        =   sylvester(number - 1     )
				lowerCAmelCase__        =   num - 1
				lowerCAmelCase__        =   num
				return lower * upper + 1


if __name__ == "__main__":
			print(F"The 8th number in Sylvester's sequence: {sylvester(8)}")




