






"""simple docstring"""



from __future__ import annotations

from random import random






class 							__SCREAMING_SNAKE_CASE						:


							def __init__(			self      :						Union[str, Any]			,    snake_case      :						int | None = None							):
													'''simple docstring'''





													A__						:  Dict		  =  value
													A__						:  Tuple		  =  random()
													A__						:  Node | None		  =  None
													A__						:  Node | None		  =  None


							def __repr__(			self      :						Optional[Any]							):
													'''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      :						Union[str, Any]							):
													'''simple docstring'''





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




def      _lowerCAmelCase		(							UpperCAmelCase__       :					Node | None,						UpperCAmelCase__       :					int      )		->tuple[Node | None, Node | None]:
						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__						:  Dict		  =  split(root.left,						UpperCAmelCase__      )
																		return left, root
												else:
																		A__  ,  A__						:  Any		  =  split(root.right,						UpperCAmelCase__      )
																		return root, right




def      _lowerCAmelCase		(							UpperCAmelCase__       :					Node | None,						UpperCAmelCase__       :					Node | None      )		->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__						:  Optional[Any]		  =  merge(left.right,						UpperCAmelCase__      )
												return left
						else:
												A__						:  Dict		  =  merge(UpperCAmelCase__,						right.left      )
												return right




def      _lowerCAmelCase		(							UpperCAmelCase__       :					Node | None,						UpperCAmelCase__       :					int      )		->Node | None:
						A__						:  Union[str, Any]		  =  Node(UpperCAmelCase__      )
						A__  ,  A__						:  List[str]		  =  split(UpperCAmelCase__,						UpperCAmelCase__      )
						return merge(merge(UpperCAmelCase__,						UpperCAmelCase__      ),						UpperCAmelCase__      )




def      _lowerCAmelCase		(							UpperCAmelCase__       :					Node | None,						UpperCAmelCase__       :					int      )		->Node | None:
						A__  ,  A__						:  Optional[int]		  =  split(UpperCAmelCase__,						value - 1      )
						A__  ,  A__						:  List[Any]		  =  split(UpperCAmelCase__,						UpperCAmelCase__      )
						return merge(UpperCAmelCase__,						UpperCAmelCase__      )




def      _lowerCAmelCase		(							UpperCAmelCase__       :					Node | None      )		->None:
						if not root:  # None
												return
						else:
												inorder(root.left      )
												print(root.value,						end=""","""      )
												inorder(root.right      )




def      _lowerCAmelCase		(							UpperCAmelCase__       :					Node | None,						UpperCAmelCase__       :					str      )		->Node | None:
						for arg in args.split():
												if arg[0] == "+":
																		A__						:  int		  =  insert(UpperCAmelCase__,						int(arg[1:]      )      )

												elif arg[0] == "-":
																		A__						:  Dict		  =  erase(UpperCAmelCase__,						int(arg[1:]      )      )

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

						return root




def      _lowerCAmelCase		(							)		->None:
						A__						:  Union[str, 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__						:  int		  =  input()
						while args != "q":
												A__						:  Dict		  =  interact_treap(UpperCAmelCase__,						UpperCAmelCase__      )
												print(UpperCAmelCase__      )
												A__						:  List[Any]		  =  input()

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


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()














"""simple docstring"""



def      _lowerCAmelCase		(							UpperCAmelCase__       :					str,						UpperCAmelCase__       :					List[Any]      )		->List[Any]:
						A__						:  Union[str, Any]		  =  [1]
						for i in range(2,						UpperCAmelCase__      ):
												factorials.append(factorials[-1] * i      )
						assert 0 <= k < factorials[-1] * n, "k out of bounds"

						A__						:  Optional[int]		  =  []
						A__						:  List[str]		  =  list(range(UpperCAmelCase__      )      )

						# Find permutation
						while factorials:
												A__						:  Optional[int]		  =  factorials.pop()
												A__  ,  A__						:  Optional[int]		  =  divmod(UpperCAmelCase__,						UpperCAmelCase__      )
												permutation.append(elements[number]      )
												elements.remove(elements[number]      )
						permutation.append(elements[0]      )

						return permutation


if __name__ == "__main__":
						import doctest

						doctest.testmod()






