
"""simple docstring"""


from __future__ import annotations

from random import random



class   __a  :






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







              """simple docstring"""
              UpperCamelCase					 =		value
              UpperCamelCase					 =		random()
              UpperCamelCase					 =		None
              UpperCamelCase					 =		None






       def __repr__(  self :							Optional[int]			)->  str:







              """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 :							Optional[Any]			)->  str:







              """simple docstring"""
              UpperCamelCase					 =		str(self.value			) + " "
              UpperCamelCase					 =		str(self.left or ""			)
              UpperCamelCase					 =		str(self.right or ""			)
              return value + left + right





def 	lowerCamelCase__			(							UpperCAmelCase_		,      UpperCAmelCase_				)->							tuple[Node | None, Node | None]:







       """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:
                     UpperCamelCase ,       UpperCamelCase					 =		split(root.left		,      UpperCAmelCase_				)
                     return left, root
              else:
                     UpperCamelCase ,       UpperCamelCase					 =		split(root.right		,      UpperCAmelCase_				)
                     return root, right



def 	lowerCamelCase__			(							UpperCAmelCase_		,      UpperCAmelCase_				)->							Node | None:







       """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:
              UpperCamelCase					 =		merge(left.right		,      UpperCAmelCase_				)
              return left
       else:
              UpperCamelCase					 =		merge(UpperCAmelCase_		,      right.left				)
              return right



def 	lowerCamelCase__			(							UpperCAmelCase_		,      UpperCAmelCase_				)->							Node | None:







       """simple docstring"""
       UpperCamelCase					 =		Node(UpperCAmelCase_				)
       UpperCamelCase ,       UpperCamelCase					 =		split(UpperCAmelCase_		,      UpperCAmelCase_				)
       return merge(merge(UpperCAmelCase_		,      UpperCAmelCase_				)		,      UpperCAmelCase_				)



def 	lowerCamelCase__			(							UpperCAmelCase_		,      UpperCAmelCase_				)->							Node | None:







       """simple docstring"""
       UpperCamelCase ,       UpperCamelCase					 =		split(UpperCAmelCase_		,      value - 1				)
       UpperCamelCase ,       UpperCamelCase					 =		split(UpperCAmelCase_		,      UpperCAmelCase_				)
       return merge(UpperCAmelCase_		,      UpperCAmelCase_				)



def 	lowerCamelCase__			(							UpperCAmelCase_				)->							None:







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



def 	lowerCamelCase__			(							UpperCAmelCase_		,      UpperCAmelCase_				)->							Node | None:







       """simple docstring"""
       for arg in args.split():
              if arg[0] == "+":
                     UpperCamelCase					 =		insert(UpperCAmelCase_		,      int(arg[1:]				)				)

              elif arg[0] == "-":
                     UpperCamelCase					 =		erase(UpperCAmelCase_		,      int(arg[1:]				)				)

              else:
                     print("Unknown command"				)

       return root



def 	lowerCamelCase__			(							)->							None:







       """simple docstring"""
       UpperCamelCase					 =		None
       print(
           "enter numbers to create a tree, + value to add value into treap, "
           "- value to erase all nodes with value. 'q' to quit. "				)

       UpperCamelCase					 =		input()
       while args != "q":
              UpperCamelCase					 =		interact_treap(UpperCAmelCase_		,      UpperCAmelCase_				)
              print(UpperCAmelCase_				)
              UpperCamelCase					 =		input()

       print("good by!"				)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()







"""simple docstring"""


def 	lowerCamelCase__			(							UpperCAmelCase_				)->							int:







       """simple docstring"""
       if a < 0:
              raise ValueError("Input value must be a positive integer"				)
       elif isinstance(UpperCAmelCase_		,      UpperCAmelCase_				):
              raise TypeError("Input value must be a 'int' type"				)
       return bin(UpperCAmelCase_				).count("1"				)


if __name__ == "__main__":
      import doctest

      doctest.testmod()





