

import itertools






def        __lowercase   (  _A = 1000000      )  ->    int:
      SCREAMING_SNAKE_CASE			:   Tuple	  = [1]

      for i in itertools.count(len(_A      )      ):
            SCREAMING_SNAKE_CASE			:   Optional[int]	  = 0
            for j in itertools.count(1      ):
                  SCREAMING_SNAKE_CASE			:   str	  = -1 if j % 2 == 0 else +1
                  SCREAMING_SNAKE_CASE			:   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(_A      )

      return 0


if __name__ == "__main__":
  import doctest

  doctest.testmod()

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







import itertools






def        __lowercase   (  _A = 1000000      )  ->    int:
      SCREAMING_SNAKE_CASE			:   Tuple	  = [1]

      for i in itertools.count(len(_A      )      ):
            SCREAMING_SNAKE_CASE			:   Optional[int]	  = 0
            for j in itertools.count(1      ):
                  SCREAMING_SNAKE_CASE			:   str	  = -1 if j % 2 == 0 else +1
                  SCREAMING_SNAKE_CASE			:   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(_A      )

      return 0


if __name__ == "__main__":
  import doctest

  doctest.testmod()

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




