

from __future__ import annotations

from random import random






class 							A_ :


     def __init__(							self			:		Tuple			,  UpperCAmelCase			:		int | None = None					)							->	Optional[Any]:
      __lowerCAmelCase:   int   	=      value
      __lowerCAmelCase:   List[str]   	=      random()
      __lowerCAmelCase:   Node | None   	=      None
      __lowerCAmelCase:   Node | None   	=      None


     def __repr__(							self			:		Optional[int]					)							->	str:
      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			:		int					)							->	str:
      __lowerCAmelCase:   str   	=      str(self.value					) + ' '
      __lowerCAmelCase:   Optional[Any]   	=      str(self.left or ''					)
      __lowerCAmelCase:   List[Any]   	=      str(self.right or ''					)
      return value + left + right







def _a (       SCREAMING_SNAKE_CASE		:			Node | None    ,					SCREAMING_SNAKE_CASE		:			int		)    ->    List[Any]:

 """simple docstring"""






 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:   Optional[Any]   	=      split(root.left    ,					SCREAMING_SNAKE_CASE		)
   return left, root
  else:
   __lowerCAmelCase:   int   	=      split(root.right    ,					SCREAMING_SNAKE_CASE		)
   return root, right







def _a (       SCREAMING_SNAKE_CASE		:			Node | None    ,					SCREAMING_SNAKE_CASE		:			Node | None		)    ->    Union[str, Any]:

 """simple docstring"""






 if (not left) or (not right):  # If one node is None, return the other
  return left or right
 elif left.prior < right.prior:
  __lowerCAmelCase:   List[str]   	=      merge(left.right    ,					SCREAMING_SNAKE_CASE		)
  return left
 else:
  __lowerCAmelCase:   List[str]   	=      merge(SCREAMING_SNAKE_CASE    ,					right.left		)
  return right







def _a (       SCREAMING_SNAKE_CASE		:			Node | None    ,					SCREAMING_SNAKE_CASE		:			int		)    ->    Tuple:

 """simple docstring"""






 __lowerCAmelCase:   Any   	=      Node(SCREAMING_SNAKE_CASE		)
 __lowerCAmelCase:   str   	=      split(SCREAMING_SNAKE_CASE    ,					SCREAMING_SNAKE_CASE		)
 return merge(merge(SCREAMING_SNAKE_CASE    ,					SCREAMING_SNAKE_CASE		)    ,					SCREAMING_SNAKE_CASE		)







def _a (       SCREAMING_SNAKE_CASE		:			Node | None    ,					SCREAMING_SNAKE_CASE		:			int		)    ->    Any:

 """simple docstring"""






 __lowerCAmelCase:   Dict   	=      split(SCREAMING_SNAKE_CASE    ,					value - 1		)
 __lowerCAmelCase:   Union[str, Any]   	=      split(SCREAMING_SNAKE_CASE    ,					SCREAMING_SNAKE_CASE		)
 return merge(SCREAMING_SNAKE_CASE    ,					SCREAMING_SNAKE_CASE		)







def _a (       SCREAMING_SNAKE_CASE		:			Node | None		)    ->    Any:

 """simple docstring"""






 if not root:  # None
  return
 else:
  inorder(root.left		)
  print(root.value    ,					end=','		)
  inorder(root.right		)







def _a (       SCREAMING_SNAKE_CASE		:			Node | None    ,					SCREAMING_SNAKE_CASE		:			str		)    ->    str:

 """simple docstring"""






 for arg in args.split():
  if arg[0] == "+":
   __lowerCAmelCase:   Optional[Any]   	=      insert(SCREAMING_SNAKE_CASE    ,					int(arg[1:]		)		)

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

  else:
   print('Unknown command'		)

 return root







def _a (       )    ->    List[str]:

 """simple docstring"""






 __lowerCAmelCase:   Optional[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:   str   	=      input()
 while args != "q":
  __lowerCAmelCase:   Dict   	=      interact_treap(SCREAMING_SNAKE_CASE    ,					SCREAMING_SNAKE_CASE		)
  print(SCREAMING_SNAKE_CASE		)
  __lowerCAmelCase:   List[str]   	=      input()

 print('good by!'		)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()










from collections import deque

from .hash_table import HashTable




class 					snake_case__						(       lowerCAmelCase_     ):






     """simple docstring"""


     def __init__(       self  :  Optional[Any], *_snake_case  :  Optional[Any], **_snake_case  :  List[Any]					)   ->Optional[int]:
            super().__init__(*_snake_case, **_snake_case					)






     def    lowercase_   (       self  :  Optional[Any], _snake_case  :  Tuple, _snake_case  :  Dict					)   ->Dict:
            snake_case__							:	int   	=	deque([]					) if self.values[key] is None else self.values[key]
            self.values[key].appendleft(_snake_case					)
            snake_case__							:	Dict   	=	self.values[key]






     def    lowercase_   (       self  :  Any					)   ->Optional[Any]:
            return (
                sum(self.charge_factor - len(_snake_case					) for slot in self.values					)
                / self.size_table
                * self.charge_factor
            )






     def    lowercase_   (       self  :  Union[str, Any], _snake_case  :  str, _snake_case  :  Optional[int]=None					)   ->Optional[Any]:
            if not (
                len(self.values[key]					) == self.charge_factor and self.values.count(_snake_case					) == 0
            ):
                   return key
            return super()._collision_resolution(_snake_case, _snake_case					)






