




"""simple docstring"""





from collections.abc import Iterable
from typing import Any



class   a__					:


			def __init__(   self   :     Dict   ,	UpperCamelCase_   :     int | None = None):


						"""simple docstring"""




						__UpperCAmelCase						:			Dict												=       value
						__UpperCAmelCase						:			Node | None												=       None  # Added in order to delete a node easier
						__UpperCAmelCase						:			Node | None												=       None
						__UpperCAmelCase						:			Node | None												=       None


			def __repr__(   self   :     Union[str, Any]):


						"""simple docstring"""




						from pprint import pformat

						if self.left is None and self.right is None:
									return str(self.value)
						return pformat({F"{self.value}": (self.left, self.right)}   ,	indent=1)






class   a__					:


			def __init__(   self   :     Tuple   ,	UpperCamelCase_   :     Node | None = None):


						"""simple docstring"""




						__UpperCAmelCase						:			int												=       root


			def __str__(   self   :     List[Any]):


						"""simple docstring"""




						return str(self.root)


			def    a_  (   self   :     Dict   ,	UpperCamelCase_   :     Node   ,	UpperCamelCase_   :     Node | None):


						"""simple docstring"""




						if new_children is not None:  # reset its kids
									__UpperCAmelCase						:			List[Any]												=       node.parent
						if node.parent is not None:  # reset its parent
									if self.is_right(UpperCamelCase_):  # If it is the right children
												__UpperCAmelCase						:			Any												=       new_children
									else:
												__UpperCAmelCase						:			List[str]												=       new_children
						else:
									__UpperCAmelCase						:			Tuple												=       new_children


			def    a_  (   self   :     Union[str, Any]   ,	UpperCamelCase_   :     Node):


						"""simple docstring"""




						if node.parent and node.parent.right:
									return node == node.parent.right
						return False


			def    a_  (   self   :     Any):


						"""simple docstring"""




						return self.root is None


			def    a_  (   self   :     int   ,	UpperCamelCase_   :     Union[str, Any]):


						"""simple docstring"""




						__UpperCAmelCase						:			Dict												=       Node(UpperCamelCase_)  # create a new Node
						if self.empty():  # if Tree is empty
									__UpperCAmelCase						:			int												=       new_node  # set its root
						else:  # Tree is not empty
									__UpperCAmelCase						:			Optional[Any]												=       self.root  # from root
									if parent_node is None:
												return
									while True:  # While we don't get to a leaf
												if value < parent_node.value:  # We go left
															if parent_node.left is None:
																		__UpperCAmelCase						:			Optional[int]												=       new_node  # We insert the new node in a leaf
																		break
															else:
																		__UpperCAmelCase						:			Any												=       parent_node.left
												else:
															if parent_node.right is None:
																		__UpperCAmelCase						:			List[str]												=       new_node
																		break
															else:
																		__UpperCAmelCase						:			Dict												=       parent_node.right
									__UpperCAmelCase						:			List[str]												=       parent_node


			def    a_  (   self   :     Any   ,	*UpperCamelCase_   :     List[Any]):


						"""simple docstring"""




						for value in values:
									self.__insert(UpperCamelCase_)


			def    a_  (   self   :     Union[str, Any]   ,	UpperCamelCase_   :     Optional[Any]):


						"""simple docstring"""




						if self.empty():
									raise IndexError("Warning: Tree is empty! please use another.")
						else:
									__UpperCAmelCase						:			Any												=       self.root
									# use lazy evaluation here to avoid NoneType Attribute error
									while node is not None and node.value is not value:
												__UpperCAmelCase						:			Tuple												=       node.left if value < node.value else node.right
									return node


			def    a_  (   self   :     Tuple   ,	UpperCamelCase_   :     Node | None = None):


						"""simple docstring"""




						if node is None:
									if self.root is None:
												return None
									__UpperCAmelCase						:			int												=       self.root

						if not self.empty():
									while node.right is not None:
												__UpperCAmelCase						:			Union[str, Any]												=       node.right
						return node


			def    a_  (   self   :     Tuple   ,	UpperCamelCase_   :     Node | None = None):


						"""simple docstring"""




						if node is None:
									__UpperCAmelCase						:			Any												=       self.root
						if self.root is None:
									return None
						if not self.empty():
									__UpperCAmelCase						:			List[str]												=       self.root
									while node.left is not None:
												__UpperCAmelCase						:			List[Any]												=       node.left
						return node


			def    a_  (   self   :     Optional[int]   ,	UpperCamelCase_   :     int):


						"""simple docstring"""




						__UpperCAmelCase						:			Optional[int]												=       self.search(UpperCamelCase_)  # Look for the node with that label
						if node is not None:
									if node.left is None and node.right is None:  # If it has no children
												self.__reassign_nodes(UpperCamelCase_   ,	UpperCamelCase_)
									elif node.left is None:  # Has only right children
												self.__reassign_nodes(UpperCamelCase_   ,	node.right)
									elif node.right is None:  # Has only left children
												self.__reassign_nodes(UpperCamelCase_   ,	node.left)
									else:
												__UpperCAmelCase						:			int												=       self.get_max(
												    node.left)  # Gets the max value of the left branch
												self.remove(tmp_node.value)  # type: ignore
												__UpperCAmelCase						:			int												=       (
												    tmp_node.value  # type: ignore
												)  # Assigns the value to the node to delete and keep tree structure


			def    a_  (   self   :     Dict   ,	UpperCamelCase_   :     Node | None):


						"""simple docstring"""




						if node is not None:
									yield node  # Preorder Traversal
									yield from self.preorder_traverse(node.left)
									yield from self.preorder_traverse(node.right)


			def    a_  (   self   :     Tuple   ,	UpperCamelCase_   :     Dict=None):


						"""simple docstring"""




						if traversal_function is None:
									return self.preorder_traverse(self.root)
						else:
									return traversal_function(self.root)


			def    a_  (   self   :     List[Any]   ,	UpperCamelCase_   :     list   ,	UpperCamelCase_   :     Node | None):


						"""simple docstring"""




						if node:
									self.inorder(UpperCamelCase_   ,	node.left)
									arr.append(node.value)
									self.inorder(UpperCamelCase_   ,	node.right)


			def    a_  (   self   :     str   ,	UpperCamelCase_   :     int   ,	UpperCamelCase_   :     Node):


						"""simple docstring"""




						__UpperCAmelCase						:			list[int]												=       []
						self.inorder(UpperCamelCase_   ,	UpperCamelCase_)  # append all values to list using inorder traversal
						return arr[k - 1]






def        _UpperCamelCase     (      UpperCamelCase				)      ->      list[Node]:


			"""simple docstring"""
			__UpperCAmelCase						:			Dict												=       []
			if curr_node is not None:
						__UpperCAmelCase						:			Union[str, Any]												=       postorder(curr_node.left				) + postorder(curr_node.right				) + [curr_node]
			return node_list

def        _UpperCamelCase     (      )      ->      None:


			"""simple docstring"""
			__UpperCAmelCase						:			Tuple												=       (8, 3, 6, 1, 10, 14, 13, 4, 7)
			__UpperCAmelCase						:			List[str]												=       BinarySearchTree()
			for i in testlist:
						t.insert(UpperCamelCase				)

			# Prints all the elements of the list in order traversal
			print(UpperCamelCase				)

			if t.search(6				) is not None:
						print("The value 6 exists"				)
			else:
						print("The value 6 doesn't exist"				)

			if t.search(-1				) is not None:
						print("The value -1 exists"				)
			else:
						print("The value -1 doesn't exist"				)

			if not t.empty():
						print("Max Value: "					,							t.get_max().value				)  # type: ignore
						print("Min Value: "					,							t.get_min().value				)  # type: ignore

			for i in testlist:
						t.remove(UpperCamelCase				)
						print(UpperCamelCase				)


if __name__ == "__main__":
					import doctest

					doctest.testmod(verbose=True)








from collections import defaultdict





def 				A__ (snake_case   :		int				)     ->						int:
					__UpperCamelCase					:	Optional[int]             =      1
					__UpperCamelCase					:	Tuple             =      True
					for v in tree[start]:
										if v not in visited:
															ret += dfs(snake_case				)
					if ret % 2 == 0:
										cuts.append(snake_case				)
					return ret





def 				A__ ()     ->						str:
					dfs(1				)


if __name__ == "__main__":
	a__     ,							a__		     =     10, 9
	a__		     =     defaultdict(list)
	a__		     =     {}
	a__		     =     []
	a__		     =     0
	a__		     =     [(2, 1), (3, 1), (4, 3), (5, 2), (6, 1), (7, 2), (8, 6), (9, 8), (10, 8)]
	for u, v in edges:
		tree[u].append(v)
		tree[v].append(u)
	even_tree()
	print(len(cuts) - 1)






