"""simple docstring"""






import itertools



def SCREAMING_SNAKE_CASE__    (     __UpperCAmelCase = 1_0_0_0_0_0_0				)						->						int:
   lowercase__:     Tuple      =   [1]

   for i in itertools.count(len(__UpperCAmelCase				)				):
      lowercase__:     Optional[Any]      =   0
      for j in itertools.count(1				):
         lowercase__:     Dict      =   -1 if j % 2 == 0 else +1
         lowercase__:     Optional[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(__UpperCAmelCase				)

   return 0


if __name__ == "__main__":
       import doctest

       doctest.testmod()

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

"""simple docstring"""






def SCREAMING_SNAKE_CASE__    (     __UpperCAmelCase				)						->						int:
   if not isinstance(__UpperCAmelCase ,					__UpperCAmelCase				):
      lowercase__:     Optional[int]      =   F"""Input value of [number={number}] must be an integer"""
      raise TypeError(__UpperCAmelCase				)
   if number < 1:
      raise ValueError('''Input must be a positive integer'''				)
   return number * (2 * number - 1)


if __name__ == "__main__":
       import doctest

       doctest.testmod()
