



"""simple docstring"""

from __future__ import annotations

from random import random




class SCREAMING_SNAKE_CASE__					:



						def __init__(self						,     _lowercase = None							):





													'''simple docstring'''

													__a		:		List[Any]									=       value
													__a		:		str									=       random()
													__a		:		Node | None									=       None
													__a		:		Node | None									=       None



						def __repr__(self							):





													'''simple docstring'''

													from pprint import pformat

													if self.left is None and self.right is None:
																				return F'''\'{self.value}: {self.prior:.5}\''''
													else:
																				return pformat(
																				    {F'''{self.value}: {self.prior:.5}''': (self.left, self.right)}						,     indent=1							)





						def __str__(self							):





													'''simple docstring'''

													__a		:		str									=       str(self.value							) + """ """
													__a		:		List[Any]									=       str(self.left or """"""							)
													__a		:		Optional[Any]									=       str(self.right or """"""							)
													return value + left + right







def       __magic_name__    (   _lowerCamelCase				: Node | None  ,       _lowerCamelCase				: int					):
							if root is None:  # None tree is split into 2 Nones
														return None, None
							elif root.value is None:
														return None, None
							else:
														if value < root.value:
																					__a							,     __a		:		Union[str, Any]									=       split(root.left  ,       _lowerCamelCase					)
																					return left, root
														else:
																					__a							,     __a		:		Any									=       split(root.right  ,       _lowerCamelCase					)
																					return root, right





def       __magic_name__    (   _lowerCamelCase				: Node | None  ,       _lowerCamelCase				: Node | None					):
							if (not left) or (not right):  # If one node is None, return the other
														return left or right
							elif left.prior < right.prior:
														__a		:		str									=       merge(left.right  ,       _lowerCamelCase					)
														return left
							else:
														__a		:		List[Any]									=       merge(_lowerCamelCase  ,       right.left					)
														return right





def       __magic_name__    (   _lowerCamelCase				: Node | None  ,       _lowerCamelCase				: int					):
							__a		:		Optional[int]									=       Node(_lowerCamelCase					)
							__a							,     __a		:		Dict									=       split(_lowerCamelCase  ,       _lowerCamelCase					)
							return merge(merge(_lowerCamelCase  ,       _lowerCamelCase					)  ,       _lowerCamelCase					)





def       __magic_name__    (   _lowerCamelCase				: Node | None  ,       _lowerCamelCase				: int					):
							__a							,     __a		:		Any									=       split(_lowerCamelCase  ,       value - 1					)
							__a							,     __a		:		List[Any]									=       split(_lowerCamelCase  ,       _lowerCamelCase					)
							return merge(_lowerCamelCase  ,       _lowerCamelCase					)





def       __magic_name__    (   _lowerCamelCase				: Node | None					):
							if not root:  # None
														return
							else:
														inorder(root.left					)
														print(root.value  ,       end=""","""					)
														inorder(root.right					)





def       __magic_name__    (   _lowerCamelCase				: Node | None  ,       _lowerCamelCase				: str					):
							for arg in args.split():
														if arg[0] == "+":
																					__a		:		Optional[int]									=       insert(_lowerCamelCase  ,       int(arg[1:]					)					)

														elif arg[0] == "-":
																					__a		:		Any									=       erase(_lowerCamelCase  ,       int(arg[1:]					)					)

														else:
																					print("""Unknown command"""					)

							return root





def       __magic_name__    (   ):
							__a		:		Optional[Any]									=       None
							print(
							    """enter numbers to create a tree, + value to add value into treap, """
							    """- value to erase all nodes with value. 'q' to quit. """					)

							__a		:		Tuple									=       input()
							while args != "q":
														__a		:		Tuple									=       interact_treap(_lowerCamelCase  ,       _lowerCamelCase					)
														print(_lowerCamelCase					)
														__a		:		Dict									=       input()

							print("""good by!"""					)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()






"""simple docstring"""

def       __magic_name__    (   _lowerCamelCase				: list[int]					):
							if not nums:  # Makes sure that the list is not empty
														raise ValueError("""List is empty"""					)

							__a		:		Any									=       sum(_lowerCamelCase					) / len(_lowerCamelCase					)  # Calculate the average
							return sum(abs(x - average					) for x in nums					) / len(_lowerCamelCase					)


if __name__ == "__main__":
	import doctest

	doctest.testmod()

