





'''simple docstring'''






from __future__ import annotations

from random import random
class 		lowerCamelCase  :



	def __init__(   self		,      a_ = None	):
							lowerCAmelCase     :    Dict						=   value
							lowerCAmelCase     :    int						=   random()
							lowerCAmelCase     :    List[Any]						=   None
							lowerCAmelCase     :    str						=   None



	def __repr__(   self	):
							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	):
							lowerCAmelCase     :    Optional[int]						=   str(self.value	) + " "
							lowerCAmelCase     :    Optional[Any]						=   str(self.left or ""	)
							lowerCAmelCase     :    Optional[int]						=   str(self.right or ""	)
							return value + left + right






def      __A						(							a_						:  Optional[Any]      ,a_						:  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:
																		lowerCAmelCase	,		lowerCAmelCase     :    Union[str, Any]						=   split(root.left      ,lowercase__	)
																		return left, root
												else:
																		lowerCAmelCase	,		lowerCAmelCase     :    Tuple						=   split(root.right      ,lowercase__	)
																		return root, right






def      __A						(							a_						:  Dict      ,a_						:  int	):
						if (not left) or (not right):  # If one node is None, return the other
												return left or right
						elif left.prior < right.prior:
												lowerCAmelCase     :    Tuple						=   merge(left.right      ,lowercase__	)
												return left
						else:
												lowerCAmelCase     :    Dict						=   merge(lowercase__      ,right.left	)
												return right






def      __A						(							a_						:  List[str]      ,a_						:  List[Any]	):
						lowerCAmelCase     :    Optional[Any]						=   Node(lowercase__	)
						lowerCAmelCase	,		lowerCAmelCase     :    Union[str, Any]						=   split(lowercase__      ,lowercase__	)
						return merge(merge(lowercase__      ,lowercase__	)      ,lowercase__	)






def      __A						(							a_						:  Optional[int]      ,a_						:  int	):
						lowerCAmelCase	,		lowerCAmelCase     :    List[Any]						=   split(lowercase__      ,value - 1	)
						lowerCAmelCase	,		lowerCAmelCase     :    Tuple						=   split(lowercase__      ,lowercase__	)
						return merge(lowercase__      ,lowercase__	)






def      __A						(							a_						:  List[str]	):
						if not root:  # None
												return
						else:
												inorder(root.left	)
												print(root.value      ,end=","	)
												inorder(root.right	)






def      __A						(							a_						:  int      ,a_						:  Tuple	):
						for arg in args.split():
												if arg[0] == "+":
																		lowerCAmelCase     :    Tuple						=   insert(lowercase__      ,int(arg[1:]	)	)

												elif arg[0] == "-":
																		lowerCAmelCase     :    str						=   erase(lowercase__      ,int(arg[1:]	)	)

												else:
																		print("Unknown command"	)

						return root






def      __A						(							):
						lowerCAmelCase     :    int						=   None
						print(
						    "enter numbers to create a tree, + value to add value into treap, "
						    "- value to erase all nodes with value. \'q\' to quit. "	)

						lowerCAmelCase     :    Any						=   input()
						while args != "q":
												lowerCAmelCase     :    Optional[Any]						=   interact_treap(lowercase__      ,lowercase__	)
												print(lowercase__	)
												lowerCAmelCase     :    int						=   input()

						print("good by!"	)


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					main()










'''simple docstring'''






import numpy as np






def      __A						(							a_						:  np.array	):
		return (2 / (1 + np.exp(-2 * vector	))) - 1


if __name__ == "__main__":
					import doctest

					doctest.testmod()



