
from math import pi, sqrt


def    a      ( a	)     ->float:




			'''simple docstring'''


			if num <= 0:
						raise ValueError('''math domain error'''	)
			if num > 1_71.5:
						raise OverflowError('''math range error'''	)
			elif num - int(a	) not in (0, 0.5):
						raise NotImplementedError('''num must be an integer or a half-integer'''	)
			elif num == 0.5:
						return sqrt(a	)
			else:
						return 1.0 if num == 1 else (num - 1) * gamma(num - 1	)


def    a      ( )     ->None:




			'''simple docstring'''


			assert gamma(0.5	) == sqrt(a	)
			assert gamma(1	) == 1.0
			assert gamma(2	) == 1.0


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

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

from collections.abc import Iterable
from typing import Any





class     lowerCamelCase      :







	def __init__(     self      :Optional[int]   ,     lowercase      :int | None = None			)		->      Optional[Any]:







				"""simple docstring"""






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







	def __repr__(     self      :Tuple			)		->      str:







				"""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      :Union[str, Any]   ,     lowercase      :Node | None = None			)		->      Dict:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= root







	def __str__(     self      :int			)		->      str:







				"""simple docstring"""






				return str(self.root			)







	def  snake_case__     (     self      :Optional[Any]   ,     lowercase      :Node   ,     lowercase      :Node | None			)		->      None:







				"""simple docstring"""






				if new_children is not None:  # reset its kids
							SCREAMING_SNAKE_CASE     						= node.parent
				if node.parent is not None:  # reset its parent
							if self.is_right(lowercase			):  # If it is the right children
										SCREAMING_SNAKE_CASE     						= new_children
							else:
										SCREAMING_SNAKE_CASE     						= new_children
				else:
							SCREAMING_SNAKE_CASE     						= new_children







	def  snake_case__     (     self      :List[str]   ,     lowercase      :Node			)		->      bool:







				"""simple docstring"""






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







	def  snake_case__     (     self      :Tuple			)		->      bool:







				"""simple docstring"""






				return self.root is None







	def  snake_case__     (     self      :Union[str, Any]   ,     lowercase      :List[Any]			)		->      None:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= Node(lowercase			)  # create a new Node
				if self.empty():  # if Tree is empty
							SCREAMING_SNAKE_CASE     						= new_node  # set its root
				else:  # Tree is not empty
							SCREAMING_SNAKE_CASE     						= 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:
																SCREAMING_SNAKE_CASE     						= new_node  # We insert the new node in a leaf
																break
													else:
																SCREAMING_SNAKE_CASE     						= parent_node.left
										else:
													if parent_node.right is None:
																SCREAMING_SNAKE_CASE     						= new_node
																break
													else:
																SCREAMING_SNAKE_CASE     						= parent_node.right
							SCREAMING_SNAKE_CASE     						= parent_node







	def  snake_case__     (     self      :Union[str, Any]   ,     *lowercase      :Optional[int]			)		->      None:







				"""simple docstring"""






				for value in values:
							self.__insert(lowercase			)







	def  snake_case__     (     self      :Union[str, Any]   ,     lowercase      :Any			)		->      Node | None:







				"""simple docstring"""






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







	def  snake_case__     (     self      :str   ,     lowercase      :Node | None = None			)		->      Node | None:







				"""simple docstring"""






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

				if not self.empty():
							while node.right is not None:
										SCREAMING_SNAKE_CASE     						= node.right
				return node







	def  snake_case__     (     self      :int   ,     lowercase      :Node | None = None			)		->      Node | None:







				"""simple docstring"""






				if node is None:
							SCREAMING_SNAKE_CASE     						= self.root
				if self.root is None:
							return None
				if not self.empty():
							SCREAMING_SNAKE_CASE     						= self.root
							while node.left is not None:
										SCREAMING_SNAKE_CASE     						= node.left
				return node







	def  snake_case__     (     self      :Optional[int]   ,     lowercase      :int			)		->      None:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= self.search(lowercase			)  # 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(lowercase   ,     lowercase			)
							elif node.left is None:  # Has only right children
										self.__reassign_nodes(lowercase   ,     node.right			)
							elif node.right is None:  # Has only left children
										self.__reassign_nodes(lowercase   ,     node.left			)
							else:
										SCREAMING_SNAKE_CASE     						= self.get_max(
										    node.left			)  # Gets the max value of the left branch
										self.remove(tmp_node.value			)  # type: ignore
										SCREAMING_SNAKE_CASE     						= (
										    tmp_node.value  # type: ignore
										)  # Assigns the value to the node to delete and keep tree structure







	def  snake_case__     (     self      :Dict   ,     lowercase      :Node | None			)		->      Iterable:







				"""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  snake_case__     (     self      :Tuple   ,     lowercase      :List[str]=None			)		->      Any:







				"""simple docstring"""






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







	def  snake_case__     (     self      :Optional[Any]   ,     lowercase      :list   ,     lowercase      :Node | None			)		->      None:







				"""simple docstring"""






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







	def  snake_case__     (     self      :Tuple   ,     lowercase      :int   ,     lowercase      :Node			)		->      int:







				"""simple docstring"""






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



def    a      ( a	)     ->list[Node]:




			'''simple docstring'''


			SCREAMING_SNAKE_CASE     						= []
			if curr_node is not None:
						SCREAMING_SNAKE_CASE     						= postorder(curr_node.left	) + postorder(curr_node.right	) + [curr_node]
			return node_list


def    a      ( )     ->None:




			'''simple docstring'''


			SCREAMING_SNAKE_CASE     						= (8, 3, 6, 1, 10, 14, 13, 4, 7)
			SCREAMING_SNAKE_CASE     						= BinarySearchTree()
			for i in testlist:
						t.insert(a	)

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

			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(a	)
						print(a	)


if __name__ == "__main__":
							import doctest

							doctest.testmod(verbose=True)