
from __future__ import annotations

from random import random
class       _lowerCAmelCase  :

 """simple docstring"""

 def __init__(						self			:			Optional[Any]					, SCREAMING_SNAKE_CASE__			:			int | None = None   ):






      """simple docstring"""



      UpperCamelCase						    =					value
      UpperCamelCase						    =					random()
      UpperCamelCase						    =					None
      UpperCamelCase						    =					None

 def __repr__(						self			:			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			:			List[str]   ):






      """simple docstring"""



      UpperCamelCase						    =					str(self.value   ) + ' '
      UpperCamelCase						    =					str(self.left or ''   )
      UpperCamelCase						    =					str(self.right or ''   )
      return value + left + right




def  __lowerCamelCase					( _lowercase						,     _lowercase			)       ->      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:
               UpperCamelCase    ,		UpperCamelCase						    =					split(root.left						,     _lowercase			)
               return left, root
          else:
               UpperCamelCase    ,		UpperCamelCase						    =					split(root.right						,     _lowercase			)
               return root, right

def  __lowerCamelCase					( _lowercase						,     _lowercase			)       ->      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:
          UpperCamelCase						    =					merge(left.right						,     _lowercase			)
          return left
     else:
          UpperCamelCase						    =					merge(_lowercase						,     right.left			)
          return right

def  __lowerCamelCase					( _lowercase						,     _lowercase			)       ->      Node | None:
     UpperCamelCase						    =					Node(_lowercase			)
     UpperCamelCase    ,		UpperCamelCase						    =					split(_lowercase						,     _lowercase			)
     return merge(merge(_lowercase						,     _lowercase			)						,     _lowercase			)

def  __lowerCamelCase					( _lowercase						,     _lowercase			)       ->      Node | None:
     UpperCamelCase    ,		UpperCamelCase						    =					split(_lowercase						,     value - 1			)
     UpperCamelCase    ,		UpperCamelCase						    =					split(_lowercase						,     _lowercase			)
     return merge(_lowercase						,     _lowercase			)

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

def  __lowerCamelCase					( _lowercase						,     _lowercase			)       ->      Node | None:
     for arg in args.split():
          if arg[0] == "+":
               UpperCamelCase						    =					insert(_lowercase						,     int(arg[1:]			)			)

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

          else:
               print('Unknown command'			)

     return root

def  __lowerCamelCase					( )       ->      None:
     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(_lowercase						,     _lowercase			)
          print(_lowercase			)
          UpperCamelCase						    =					input()

     print('good by!'			)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 main()




def  __lowerCamelCase					( _lowercase			)       ->      list:
     for i in range(len(_lowercase			) - 1						,     0						,     -1			):
          UpperCamelCase						    =					False

          for j in range(_lowercase						,     0						,     -1			):
               if unsorted[j] < unsorted[j - 1]:
                    UpperCamelCase    ,		UpperCamelCase						    =					unsorted[j - 1], unsorted[j]
                    UpperCamelCase						    =					True

          for j in range(_lowercase			):
               if unsorted[j] > unsorted[j + 1]:
                    UpperCamelCase    ,		UpperCamelCase						    =					unsorted[j + 1], unsorted[j]
                    UpperCamelCase						    =					True

          if not swapped:
               break
     return unsorted


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 _snake_case      = input('''Enter numbers separated by a comma:\n''').strip()
 _snake_case      = [int(item) for item in user_input.split(''',''')]
 print(F"{cocktail_shaker_sort(unsorted) = }")


