


"""simple docstring"""




from __future__ import annotations

import queue




class 			__snake_case   :




							def __init__(     self:    List[str]     ,							A_:    Tuple   ):
										__lowerCamelCase          =      data
										__lowerCamelCase          =      None
										__lowerCamelCase          =      None





def       a_ (	):
			print("""\n********Press N to stop entering at any point of time********\n"""     )
			__lowerCamelCase          =      input("""Enter the value of the root node: """     ).strip().lower()
			__lowerCamelCase          =      queue.Queue()
			__lowerCamelCase          =      TreeNode(int(lowercase__     )     )
			q.put(lowercase__     )
			while not q.empty():
						__lowerCamelCase          =      q.get()
						__lowerCamelCase          =      f'Enter the left node of {node_found.data}: '
						__lowerCamelCase          =      input(lowercase__     ).strip().lower() or """n"""
						if check == "n":
									return tree_node
						__lowerCamelCase          =      TreeNode(int(lowercase__     )     )
						__lowerCamelCase          =      left_node
						q.put(lowercase__     )
						__lowerCamelCase          =      f'Enter the right node of {node_found.data}: '
						__lowerCamelCase          =      input(lowercase__     ).strip().lower() or """n"""
						if check == "n":
									return tree_node
						__lowerCamelCase          =      TreeNode(int(lowercase__     )     )
						__lowerCamelCase          =      right_node
						q.put(lowercase__     )
			raise





def       a_ (	lowercase__ :TreeNode     ):
			if not isinstance(lowercase__,			lowercase__     ) or not node:
						return
			print(node.data,			end=""","""     )
			pre_order(node.left     )
			pre_order(node.right     )





def       a_ (	lowercase__ :TreeNode     ):
			if not isinstance(lowercase__,			lowercase__     ) or not node:
						return
			in_order(node.left     )
			print(node.data,			end=""","""     )
			in_order(node.right     )





def       a_ (	lowercase__ :TreeNode     ):
			if not isinstance(lowercase__,			lowercase__     ) or not node:
						return
			post_order(node.left     )
			post_order(node.right     )
			print(node.data,			end=""","""     )





def       a_ (	lowercase__ :TreeNode     ):
			if not isinstance(lowercase__,			lowercase__     ) or not node:
						return
			__lowerCamelCase          =      queue.Queue()
			q.put(lowercase__     )
			while not q.empty():
						__lowerCamelCase          =      q.get()
						print(node_dequeued.data,			end=""","""     )
						if node_dequeued.left:
									q.put(node_dequeued.left     )
						if node_dequeued.right:
									q.put(node_dequeued.right     )





def       a_ (	lowercase__ :TreeNode     ):
			if not isinstance(lowercase__,			lowercase__     ) or not node:
						return
			__lowerCamelCase          =      queue.Queue()
			q.put(lowercase__     )
			while not q.empty():
						__lowerCamelCase          =      []
						while not q.empty():
									__lowerCamelCase          =      q.get()
									print(node_dequeued.data,			end=""","""     )
									if node_dequeued.left:
												list_.append(node_dequeued.left     )
									if node_dequeued.right:
												list_.append(node_dequeued.right     )
						print()
						for node in list_:
									q.put(lowercase__     )





def       a_ (	lowercase__ :TreeNode     ):
			if not isinstance(lowercase__,			lowercase__     ) or not node:
						return
			__lowerCamelCase          =      []
			__lowerCamelCase          =      node
			while n or stack:
						while n:  # start from root node, find its left child
									print(n.data,			end=""","""     )
									stack.append(lowercase__     )
									__lowerCamelCase          =      n.left
						# end of while means current node doesn't have left child
						__lowerCamelCase          =      stack.pop()
						# start to traverse its right child
						__lowerCamelCase          =      n.right





def       a_ (	lowercase__ :TreeNode     ):
			if not isinstance(lowercase__,			lowercase__     ) or not node:
						return
			__lowerCamelCase          =      []
			__lowerCamelCase          =      node
			while n or stack:
						while n:
									stack.append(lowercase__     )
									__lowerCamelCase          =      n.left
						__lowerCamelCase          =      stack.pop()
						print(n.data,			end=""","""     )
						__lowerCamelCase          =      n.right





def       a_ (	lowercase__ :TreeNode     ):
			if not isinstance(lowercase__,			lowercase__     ) or not node:
						return
			__lowerCamelCase     ,__lowerCamelCase          =      [], []
			__lowerCamelCase          =      node
			stacka.append(lowercase__     )
			while stacka:  # to find the reversed order of post order, store it in stack2
						__lowerCamelCase          =      stacka.pop()
						if n.left:
									stacka.append(n.left     )
						if n.right:
									stacka.append(n.right     )
						stacka.append(lowercase__     )
			while stacka:  # pop up from stack2 will be the post order
						print(stacka.pop().data,			end=""","""     )





def       a_ (	lowercase__ :str = "",			lowercase__ :Optional[Any]=50,			lowercase__ :List[Any]="*"     ):
			if not s:
						return "\n" + width * char
			__lowerCamelCase     ,__lowerCamelCase          =      divmod(width - len(lowercase__     ) - 2,			2     )
			return f'{left * char} {s} {(left + extra) * char}'


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					print(prompt('Binary Tree Traversals'))

					__magic_name__						: TreeNode    =				build_tree()
					print(prompt('Pre Order Traversal'))
					pre_order(node)
					print(prompt() + '\n')

					print(prompt('In Order Traversal'))
					in_order(node)
					print(prompt() + '\n')

					print(prompt('Post Order Traversal'))
					post_order(node)
					print(prompt() + '\n')

					print(prompt('Level Order Traversal'))
					level_order(node)
					print(prompt() + '\n')

					print(prompt('Actual Level Order Traversal'))
					level_order_actual(node)
					print('*' * 5_0 + '\n')

					print(prompt('Pre Order Traversal - Iteration Version'))
					pre_order_iter(node)
					print(prompt() + '\n')

					print(prompt('In Order Traversal - Iteration Version'))
					in_order_iter(node)
					print(prompt() + '\n')

					print(prompt('Post Order Traversal - Iteration Version'))
					post_order_iter(node)
					print(prompt())








"""simple docstring"""




from collections import defaultdict





def       a_ (	lowercase__ :int     ):
			__lowerCamelCase          =      1
			__lowerCamelCase          =      True
			for v in tree[start]:
						if v not in visited:
									ret += dfs(lowercase__     )
			if ret % 2 == 0:
						cuts.append(lowercase__     )
			return ret





def       a_ (	):
			dfs(1     )


if __name__ == "__main__":
					__magic_name__  , __magic_name__						: Tuple    =				1_0, 9
					__magic_name__						: Tuple    =				defaultdict(list)
					__magic_name__						: dict[int, bool]    =				{}
					__magic_name__						: list[int]    =				[]
					__magic_name__						: List[str]    =				0
					__magic_name__						: Tuple    =				[(2, 1), (3, 1), (4, 3), (5, 2), (6, 1), (7, 2), (8, 6), (9, 8), (1_0, 8)]
					for u, v in edges:
										tree[u].append(v)
										tree[v].append(u)
					even_tree()
					print(len(cuts) - 1)




