


'''simple docstring'''







from __future__ import annotations

from random import random
class 						UpperCamelCase__       :



     """simple docstring"""






     def __init__(			self   ,						snake_case__ = None ):

            '''simple docstring'''

            _lowerCAmelCase     :				Union[str, Any]       =							value
            _lowerCAmelCase     :				int       =							random()
            _lowerCAmelCase     :				Node | None       =							None
            _lowerCAmelCase     :				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'''

            _lowerCAmelCase     :				str       =							str(self.value ) + ' '
            _lowerCAmelCase     :				Dict       =							str(self.left or '' )
            _lowerCAmelCase     :				List[Any]       =							str(self.right or '' )
            return value + left + right






def       lowercase					(_A ,    _A       ):







       """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      ,  _lowerCAmelCase     :				str       =							split(root.left ,    _A       )
                     return left, root
              else:
                     _lowerCAmelCase      ,  _lowerCAmelCase     :				Dict       =							split(root.right ,    _A       )
                     return root, right






def       lowercase					(_A ,    _A       ):







       """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     :				int       =							merge(left.right ,    _A       )
              return left
       else:
              _lowerCAmelCase     :				List[str]       =							merge(_A ,    right.left       )
              return right






def       lowercase					(_A ,    _A       ):







       """simple docstring"""







       _lowerCAmelCase     :				Tuple       =							Node(_A       )
       _lowerCAmelCase      ,  _lowerCAmelCase     :				Tuple       =							split(_A ,    _A       )
       return merge(merge(_A ,    _A       ) ,    _A       )






def       lowercase					(_A ,    _A       ):







       """simple docstring"""







       _lowerCAmelCase      ,  _lowerCAmelCase     :				List[str]       =							split(_A ,    value - 1       )
       _lowerCAmelCase      ,  _lowerCAmelCase     :				Union[str, Any]       =							split(_A ,    _A       )
       return merge(_A ,    _A       )






def       lowercase					(_A       ):







       """simple docstring"""







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






def       lowercase					(_A ,    _A       ):







       """simple docstring"""







       for arg in args.split():
              if arg[0] == "+":
                     _lowerCAmelCase     :				Dict       =							insert(_A ,    int(arg[1:]       )       )

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

              else:
                     print('Unknown command'       )

       return root






def       lowercase					():







       """simple docstring"""







       _lowerCAmelCase     :				List[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. '       )

       _lowerCAmelCase     :				Tuple       =							input()
       while args != "q":
              _lowerCAmelCase     :				Optional[Any]       =							interact_treap(_A ,    _A       )
              print(_A       )
              _lowerCAmelCase     :				str       =							input()

       print('good by!'       )


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       main()





'''simple docstring'''







from __future__ import annotations

from collections.abc import Iterator
class 						UpperCamelCase__       :



     """simple docstring"""






     def __init__(			self   ,						snake_case__ ):

            '''simple docstring'''

            _lowerCAmelCase     :				List[Any]       =							value
            _lowerCAmelCase     :				Node | None       =							None
            _lowerCAmelCase     :				Node | None       =							None
class 						UpperCamelCase__       :



     """simple docstring"""






     def __init__(			self   ,						snake_case__ ):

            '''simple docstring'''

            _lowerCAmelCase     :				List[Any]       =							tree







     def a						(			self   ,						snake_case__ ):

            '''simple docstring'''

            if node is None:
                   return 0
            return node.value + (
                self.depth_first_search(node.left ) + self.depth_first_search(node.right )
            )







     def __iter__(			self ):

            '''simple docstring'''

            yield self.depth_first_search(self.tree )


if __name__ == "__main__":
       import doctest

       doctest.testmod()

