



from __future__ import annotations

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



@dataclass
class 				__snake_case						:
							_a			      = 42
							_a			      = None
							_a			      = None





def 			UpperCamelCase(  ):
		lowerCAmelCase_			:     Any									= Node(1 )
		lowerCAmelCase_			:     List[str]									= Node(2 )
		lowerCAmelCase_			:     Optional[Any]									= Node(3 )
		lowerCAmelCase_			:     int									= Node(4 )
		lowerCAmelCase_			:     Any									= Node(5 )
		return tree


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


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


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


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


def 			UpperCamelCase(  __UpperCamelCase							:		Node | None ):
		lowerCAmelCase_			:     list[Any]									= []

		if root is None:
				return output

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

		while process_queue:
				lowerCAmelCase_			:     Optional[int]									= 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(  __UpperCamelCase							:		Node | None     ,__UpperCamelCase							:		int ):
		lowerCAmelCase_			:     list[Any]									= []

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


def 			UpperCamelCase(  __UpperCamelCase							:		Node | None     ,__UpperCamelCase							:		int ):
		lowerCAmelCase_			:     list[Any]									= []

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


def 			UpperCamelCase(  __UpperCamelCase							:		Node | None ):
		if root is None:
				return []

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

		lowerCAmelCase_			:     Any									= 0
		lowerCAmelCase_			:     List[str]									= height(__UpperCamelCase )

		for h in range(1     ,height_tree + 1 ):
				if not flag:
						output.append(get_nodes_from_left_to_right(__UpperCamelCase     ,__UpperCamelCase ) )
						lowerCAmelCase_			:     str									= 1
				else:
						output.append(get_nodes_from_right_to_left(__UpperCamelCase     ,__UpperCamelCase ) )
						lowerCAmelCase_			:     Optional[Any]									= 0

		return output


def 			UpperCamelCase(  ):  # Main function for testing.
		lowerCAmelCase_			:     Any									= 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()










_lowercase: Dict      			=		[
    (1000, "M"),
    (900, "CM"),
    (500, "D"),
    (400, "CD"),
    (100, "C"),
    (90, "XC"),
    (50, "L"),
    (40, "XL"),
    (10, "X"),
    (9, "IX"),
    (5, "V"),
    (4, "IV"),
    (1, "I"),
]






def     a(      A       :    str       )		->       int:
					"""simple docstring"""





					a					     =   {"I": 1, "V": 5, "X": 10, "L": 50, "C": 100, "D": 500, "M": 1000}
					a					     =   0
					a					     =   0
					while place < len(A       ):
										if (place + 1 < len(A       )) and (vals[roman[place]] < vals[roman[place + 1]]):
															total += vals[roman[place + 1]] - vals[roman[place]]
															place += 2
										else:
															total += vals[roman[place]]
															place += 1
					return total






def     a(      A       :    int       )		->       str:
					"""simple docstring"""





					a					     =   []
					for arabic, roman in ROMAN:
										((a)     ,				(a))					     =   divmod(A ,     A       )
										result.append(roman * factor       )
										if number == 0:
															break
					return "".join(A       )


if __name__ == "__main__":
				import doctest

				doctest.testmod()
