





def       _A  (      ):
   for n in range(1							, 100_0000   ):
      yield n * (n + 1) // 2






def       _A  (      lowerCamelCase   ):
   a__	:						Optional[int]      		=  1
   a__	:						Any      		=  2
   while i * i <= n:
      a__	:						List[str]      		=  0
      while n % i == 0:
         n //= i
         multiplicity += 1
      divisors_count *= multiplicity + 1
      i += 1
   if n > 1:
      divisors_count *= 2
   return divisors_count






def       _A  (      ):
   return next(i for i in triangle_number_generator() if count_divisors(lowerCamelCase   ) > 500   )


if __name__ == "__main__":
  print(solution())








from __future__ import annotations

from random import random







class   __lowerCAmelCase			:





   def __init__( self					,			snake_case = None      )				->  Any:
      """simple docstring"""





      a__	:						Optional[int]      		=  value
      a__	:						Tuple      		=  random()
      a__	:						Node | None      		=  None
      a__	:						Node | None      		=  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"""





      a__	:						List[Any]      		=  str(self.value      ) + " "
      a__	:						List[str]      		=  str(self.left or ""      )
      a__	:						Tuple      		=  str(self.right or ""      )
      return value + left + right







def       _A  (      lowerCamelCase							, lowerCamelCase   ):
   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:
         a__		,     a__	:						Dict      		=  split(root.left							, lowerCamelCase   )
         return left, root
      else:
         a__		,     a__	:						int      		=  split(root.right							, lowerCamelCase   )
         return root, right






def       _A  (      lowerCamelCase							, lowerCamelCase   ):
   if (not left) or (not right):  # If one node is None, return the other
      return left or right
   elif left.prior < right.prior:
      a__	:						List[Any]      		=  merge(left.right							, lowerCamelCase   )
      return left
   else:
      a__	:						int      		=  merge(lowerCamelCase							, right.left   )
      return right






def       _A  (      lowerCamelCase							, lowerCamelCase   ):
   a__	:						Any      		=  Node(lowerCamelCase   )
   a__		,     a__	:						List[str]      		=  split(lowerCamelCase							, lowerCamelCase   )
   return merge(merge(lowerCamelCase							, lowerCamelCase   )							, lowerCamelCase   )






def       _A  (      lowerCamelCase							, lowerCamelCase   ):
   a__		,     a__	:						Optional[int]      		=  split(lowerCamelCase							, value - 1   )
   a__		,     a__	:						Tuple      		=  split(lowerCamelCase							, lowerCamelCase   )
   return merge(lowerCamelCase							, lowerCamelCase   )






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






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

      elif arg[0] == "-":
         a__	:						Union[str, Any]      		=  erase(lowerCamelCase							, int(arg[1:]   )   )

      else:
         print("Unknown command"   )

   return root






def       _A  (      ):
   a__	:						List[str]      		=  None
   print(
       "enter numbers to create a tree, + value to add value into treap, "
       "- value to erase all nodes with value. 'q' to quit. "   )

   a__	:						int      		=  input()
   while args != "q":
      a__	:						Union[str, Any]      		=  interact_treap(lowerCamelCase							, lowerCamelCase   )
      print(lowerCamelCase   )
      a__	:						Optional[Any]      		=  input()

   print("good by!"   )


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()

