





from __future__ import annotations

from random import random

class 		SCREAMING_SNAKE_CASE__				:


      def __init__(self       :      int				,			a__       :      int | None = None      ):





         """simple docstring"""



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


      def __repr__(self       :      List[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       :      int      ):





         """simple docstring"""



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






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






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






def lowerCamelCase__    (							snake_case_	:  Node | None       ,      snake_case_	:  int       )      ->				Node | None:
   __snake_case							       =   Node(snake_case_       )
   __snake_case       ,	__snake_case							       =   split(snake_case_       ,      snake_case_       )
   return merge(merge(snake_case_       ,      snake_case_       )       ,      snake_case_       )






def lowerCamelCase__    (							snake_case_	:  Node | None       ,      snake_case_	:  int       )      ->				Node | None:
   __snake_case       ,	__snake_case							       =   split(snake_case_       ,      value - 1       )
   __snake_case       ,	__snake_case							       =   split(snake_case_       ,      snake_case_       )
   return merge(snake_case_       ,      snake_case_       )






def lowerCamelCase__    (							snake_case_	:  Node | None       )      ->				None:
   if not root:  # None
      return
   else:
      inorder(root.left       )
      print(root.value       ,      end=''','''       )
      inorder(root.right       )






def lowerCamelCase__    (							snake_case_	:  Node | None       ,      snake_case_	:  str       )      ->				Node | None:
   for arg in args.split():
      if arg[0] == "+":
         __snake_case							       =   insert(snake_case_       ,      int(arg[1:]       )       )

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

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

   return root






def lowerCamelCase__    (							)      ->				None:
   __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(snake_case_       ,      snake_case_       )
      print(snake_case_       )
      __snake_case							       =   input()

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


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    main()








from math import pi






def lowerCamelCase__    (							snake_case_	:  int       ,      snake_case_	:  int       )      ->				float:
   return 2 * pi * radius * (angle / 360)


if __name__ == "__main__":
    print(arc_length(90, 10))

