




from collections.abc import Iterable
from typing import Any

class 		__lowerCAmelCase	:
							def __init__(						self						:List[str]		,      __magic_name__						:int | None = None				):







								'''simple docstring'''







								a										=							value
								a										=							None  # Added in order to delete a node easier
								a										=							None
								a										=							None





							def __repr__(						self						:int				):







								'''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 		__lowerCAmelCase	:
							def __init__(						self						:int		,      __magic_name__						:Node | None = None				):







								'''simple docstring'''







								a										=							root
							def __str__(						self						:Any				):







								'''simple docstring'''







								return str(self.root				)
							def       lowerCamelCase__							(						self						:Any		,      __magic_name__						:Node		,      __magic_name__						:Node | None				):







								'''simple docstring'''







								if new_children is not None:  # reset its kids
									a										=							node.parent
								if node.parent is not None:  # reset its parent
									if self.is_right(__magic_name__				):  # If it is the right children
										a										=							new_children
									else:
										a										=							new_children
								else:
									a										=							new_children
							def       lowerCamelCase__							(						self						:Union[str, Any]		,      __magic_name__						:Node				):







								'''simple docstring'''







								if node.parent and node.parent.right:
									return node == node.parent.right
								return False
							def       lowerCamelCase__							(						self						:int				):







								'''simple docstring'''







								return self.root is None
							def       lowerCamelCase__							(						self						:int		,      __magic_name__						:Any				):







								'''simple docstring'''







								a										=							Node(__magic_name__				)  # create a new Node
								if self.empty():  # if Tree is empty
									a										=							new_node  # set its root
								else:  # Tree is not empty
									a										=							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:
												a										=							new_node  # We insert the new node in a leaf
												break
											else:
												a										=							parent_node.left
										else:
											if parent_node.right is None:
												a										=							new_node
												break
											else:
												a										=							parent_node.right
									a										=							parent_node
							def       lowerCamelCase__							(						self						:Optional[Any]		,      *__magic_name__						:Dict				):







								'''simple docstring'''







								for value in values:
									self.__insert(__magic_name__				)
							def       lowerCamelCase__							(						self						:List[Any]		,      __magic_name__						:int				):







								'''simple docstring'''







								if self.empty():
									raise IndexError("""Warning: Tree is empty! please use another."""				)
								else:
									a										=							self.root
									# use lazy evaluation here to avoid NoneType Attribute error
									while node is not None and node.value is not value:
										a										=							node.left if value < node.value else node.right
									return node
							def       lowerCamelCase__							(						self						:Union[str, Any]		,      __magic_name__						:Node | None = None				):







								'''simple docstring'''







								if node is None:
									if self.root is None:
										return None
									a										=							self.root

								if not self.empty():
									while node.right is not None:
										a										=							node.right
								return node
							def       lowerCamelCase__							(						self						:List[Any]		,      __magic_name__						:Node | None = None				):







								'''simple docstring'''







								if node is None:
									a										=							self.root
								if self.root is None:
									return None
								if not self.empty():
									a										=							self.root
									while node.left is not None:
										a										=							node.left
								return node
							def       lowerCamelCase__							(						self						:Optional[Any]		,      __magic_name__						:int				):







								'''simple docstring'''







								a										=							self.search(__magic_name__				)  # 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(__magic_name__		,      __magic_name__				)
									elif node.left is None:  # Has only right children
										self.__reassign_nodes(__magic_name__		,      node.right				)
									elif node.right is None:  # Has only left children
										self.__reassign_nodes(__magic_name__		,      node.left				)
									else:
										a										=							self.get_max(
										    node.left				)  # Gets the max value of the left branch
										self.remove(tmp_node.value				)  # type: ignore
										a										=							(
										    tmp_node.value  # type: ignore
										)  # Assigns the value to the node to delete and keep tree structure
							def       lowerCamelCase__							(						self						:Optional[int]		,      __magic_name__						: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       lowerCamelCase__							(						self						:str		,      __magic_name__						:Tuple=None				):







								'''simple docstring'''







								if traversal_function is None:
									return self.preorder_traverse(self.root				)
								else:
									return traversal_function(self.root				)
							def       lowerCamelCase__							(						self						:Optional[int]		,      __magic_name__						:list		,      __magic_name__						:Node | None				):







								'''simple docstring'''







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





							def       lowerCamelCase__							(						self						:List[str]		,      __magic_name__						:int		,      __magic_name__						:Node				):







								'''simple docstring'''







								a										=							[]
								self.inorder(__magic_name__		,      __magic_name__				)  # append all values to list using inorder traversal
								return arr[k - 1]







def 		__A		(	__lowerCamelCase    )      ->       list[Node]:
	a										=							[]
	if curr_node is not None:
		a										=							postorder(curr_node.left    ) + postorder(curr_node.right    ) + [curr_node]
	return node_list





def 		__A		(	)      ->       None:
	a										=							(8, 3, 6, 1, 10, 14, 13, 4, 7)
	a										=							BinarySearchTree()
	for i in testlist:
		t.insert(__lowerCamelCase    )

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

	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(__lowerCamelCase    )
		print(__lowerCamelCase    )


if __name__ == "__main__":
		import doctest

		doctest.testmod(verbose=True)







from math import pi, sqrt





def 		__A		(	__lowerCamelCase    )      ->       float:
	if num <= 0:
		raise ValueError("""math domain error"""    )
	if num > 171.5:
		raise OverflowError("""math range error"""    )
	elif num - int(__lowerCamelCase    ) not in (0, 0.5):
		raise NotImplementedError("""num must be an integer or a half-integer"""    )
	elif num == 0.5:
		return sqrt(__lowerCamelCase    )
	else:
		return 1.0 if num == 1 else (num - 1) * gamma(num - 1    )





def 		__A		(	)      ->       None:
	assert gamma(0.5    ) == sqrt(__lowerCamelCase    )
	assert gamma(1    ) == 1.0
	assert gamma(2    ) == 1.0


if __name__ == "__main__":
		from doctest import testmod

		testmod()
		__UpperCamelCase					:       str    					=      1.0
		while num:
				__UpperCamelCase					:       Dict    					=      float(input("Gamma of: "))
				print(F'gamma({num}) = {gamma(num)}')
				print("\nEnter 0 to exit...")

