




'''simple docstring'''



from __future__ import annotations

from random import random





class      lowerCAmelCase :


       def __init__( self     ,	__SCREAMING_SNAKE_CASE = None	)   ->	Any:



            '''simple docstring'''




            __snake_case            =	value
            __snake_case            =	random()
            __snake_case            =	None
            __snake_case            =	None


       def __repr__( self	)   ->	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	)   ->	str:



            '''simple docstring'''




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







def       _UpperCamelCase			(_lowerCamelCase				:  Node | None ,						_lowerCamelCase				:  int						)-> 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:
               __snake_case       ,     __snake_case            =	split(root.left ,						_lowerCamelCase						)
               return left, root
          else:
               __snake_case       ,     __snake_case            =	split(root.right ,						_lowerCamelCase						)
               return root, right







def       _UpperCamelCase			(_lowerCamelCase				:  Node | None ,						_lowerCamelCase				:  Node | None						)-> 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:
          __snake_case            =	merge(left.right ,						_lowerCamelCase						)
          return left
     else:
          __snake_case            =	merge(_lowerCamelCase ,						right.left						)
          return right







def       _UpperCamelCase			(_lowerCamelCase				:  Node | None ,						_lowerCamelCase				:  int						)-> Node | None:




     '''simple docstring'''





     __snake_case            =	Node(_lowerCamelCase						)
     __snake_case       ,     __snake_case            =	split(_lowerCamelCase ,						_lowerCamelCase						)
     return merge(merge(_lowerCamelCase ,						_lowerCamelCase						) ,						_lowerCamelCase						)







def       _UpperCamelCase			(_lowerCamelCase				:  Node | None ,						_lowerCamelCase				:  int						)-> Node | None:




     '''simple docstring'''





     __snake_case       ,     __snake_case            =	split(_lowerCamelCase ,						value - 1						)
     __snake_case       ,     __snake_case            =	split(_lowerCamelCase ,						_lowerCamelCase						)
     return merge(_lowerCamelCase ,						_lowerCamelCase						)







def       _UpperCamelCase			(_lowerCamelCase				:  Node | None						)-> None:




     '''simple docstring'''





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







def       _UpperCamelCase			(_lowerCamelCase				:  Node | None ,						_lowerCamelCase				:  str						)-> Node | None:




     '''simple docstring'''





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

          elif arg[0] == "-":
               __snake_case            =	erase(_lowerCamelCase ,						int(arg[1:]						)						)

          else:
               print('''Unknown command'''						)

     return root







def       _UpperCamelCase			()-> None:




     '''simple docstring'''





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

     __snake_case            =	input()
     while args != "q":
          __snake_case            =	interact_treap(_lowerCamelCase ,						_lowerCamelCase						)
          print(_lowerCamelCase						)
          __snake_case            =	input()

     print('''good by!'''						)


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     main()












'''simple docstring'''



def       _UpperCamelCase			(_lowerCamelCase				:  Optional[Any]						)-> Dict:




     '''simple docstring'''





     __snake_case            =	[]
     __snake_case            =	[]
     __snake_case            =	{
         '''^''': 3,
         '''*''': 2,
         '''/''': 2,
         '''%''': 2,
         '''+''': 1,
         '''-''': 1,
     }  # Priority of each operator
     __snake_case            =	len(_lowerCamelCase						) if (len(_lowerCamelCase						) > 7) else 7

     # Print table header for output
     print(
         '''Symbol'''.center(8						) ,						'''Stack'''.center(_lowerCamelCase						) ,						'''Postfix'''.center(_lowerCamelCase						) ,						sep=''' | ''' ,						)
     print('''-''' * (print_width * 3 + 7)						)

     for x in infix:
          if x.isalpha() or x.isdigit():
               post_fix.append(_lowerCamelCase						)  # if x is Alphabet / Digit, add it to Postfix
          elif x == "(":
               stack.append(_lowerCamelCase						)  # if x is "(" push to Stack
          elif x == ")":  # if x is ")" pop stack until "(" is encountered
               while stack[-1] != "(":
                    post_fix.append(stack.pop()						)  # Pop stack & add the content to Postfix
               stack.pop()
          else:
               if len(_lowerCamelCase						) == 0:
                    stack.append(_lowerCamelCase						)  # If stack is empty, push x to stack
               else:  # while priority of x is not > priority of element in the stack
                    while len(_lowerCamelCase						) > 0 and priority[x] <= priority[stack[-1]]:
                         post_fix.append(stack.pop()						)  # pop stack & add to Postfix
                    stack.append(_lowerCamelCase						)  # push x to stack

          print(
              x.center(8						) ,						(''''''.join(_lowerCamelCase						)).ljust(_lowerCamelCase						) ,						(''''''.join(_lowerCamelCase						)).ljust(_lowerCamelCase						) ,						sep=''' | ''' ,						)  # Output in tabular format

     while len(_lowerCamelCase						) > 0:  # while stack is not empty
          post_fix.append(stack.pop()						)  # pop stack & add to Postfix
          print(
              ''' '''.center(8						) ,						(''''''.join(_lowerCamelCase						)).ljust(_lowerCamelCase						) ,						(''''''.join(_lowerCamelCase						)).ljust(_lowerCamelCase						) ,						sep=''' | ''' ,						)  # Output in tabular format

     return "".join(_lowerCamelCase						)  # return Postfix as str







def       _UpperCamelCase			(_lowerCamelCase				:  Optional[Any]						)-> str:




     '''simple docstring'''





     __snake_case            =	list(infix[::-1]						)  # reverse the infix equation

     for i in range(len(_lowerCamelCase						)						):
          if infix[i] == "(":
               __snake_case            =	''')'''  # change "(" to ")"
          elif infix[i] == ")":
               __snake_case            =	'''('''  # change ")" to "("

     return (infix_2_postfix(''''''.join(_lowerCamelCase						)						))[
         ::-1
     ]  # call infix_2_postfix on Infix, return reverse of Postfix


if __name__ == "__main__":
     UpperCAmelCase_							:	Dict	     =		input('''\nEnter an Infix Equation = ''')  # Input an Infix equation
     UpperCAmelCase_							:	Optional[Any]	     =		''''''.join(Infix.split())  # Remove spaces from the input
     print('''\n\t''', Infix, '''(Infix) -> ''', infix_2_prefix(Infix), '''(Prefix)''')






