

'''simple docstring'''






import itertools


def 					__lowerCamelCase			(      SCREAMING_SNAKE_CASE_     :	int = 1_0_0_0_0_0_0    )							->   int:
      """simple docstring"""

      SCREAMING_SNAKE_CASE_      :			Union[str, Any]     =       [1]

      for i in itertools.count(len(SCREAMING_SNAKE_CASE_    )    ):
            SCREAMING_SNAKE_CASE_      :			Any     =       0
            for j in itertools.count(1    ):
                  SCREAMING_SNAKE_CASE_      :			int     =       -1 if j % 2 == 0 else +1
                  SCREAMING_SNAKE_CASE_      :			Union[str, Any]     =       (j * j * 3 - j) // 2
                  if index > i:
                        break
                  item += partitions[i - index] * sign
                  item %= number
                  index += j
                  if index > i:
                        break
                  item += partitions[i - index] * sign
                  item %= number

            if item == 0:
                  return i
            partitions.append(SCREAMING_SNAKE_CASE_    )

      return 0


if __name__ == "__main__":
      import doctest

      doctest.testmod()

      print(F'''{solution() = }''')




'''simple docstring'''






from ..utils import DummyObject, requires_backends
class 	SCREAMING_SNAKE_CASE__			(				metaclass=_UpperCAmelCase      ):
    _A			    =							["torch", "transformers", "invisible_watermark"]




    def __init__(					self				,     *lowercase__				,     **lowercase__			):






          """simple docstring"""






          requires_backends(self				,     ["torch", "transformers", "invisible_watermark"]			)




    @classmethod
    def   __lowerCamelCase      (					cls				,     *lowercase__				,     **lowercase__			):






          """simple docstring"""






          requires_backends(cls				,     ["torch", "transformers", "invisible_watermark"]			)







    @classmethod
    def   __lowerCamelCase      (					cls				,     *lowercase__				,     **lowercase__			):






          """simple docstring"""






          requires_backends(cls				,     ["torch", "transformers", "invisible_watermark"]			)






class 	SCREAMING_SNAKE_CASE__			(				metaclass=_UpperCAmelCase      ):
    _A			    =							["torch", "transformers", "invisible_watermark"]




    def __init__(					self				,     *lowercase__				,     **lowercase__			):






          """simple docstring"""






          requires_backends(self				,     ["torch", "transformers", "invisible_watermark"]			)




    @classmethod
    def   __lowerCamelCase      (					cls				,     *lowercase__				,     **lowercase__			):






          """simple docstring"""






          requires_backends(cls				,     ["torch", "transformers", "invisible_watermark"]			)







    @classmethod
    def   __lowerCamelCase      (					cls				,     *lowercase__				,     **lowercase__			):






          """simple docstring"""






          requires_backends(cls				,     ["torch", "transformers", "invisible_watermark"]			)

