






'''simple docstring'''







def     A__      (					__lowerCAmelCase		:      int    ):
						lowerCamelCase__								=	(1 + 24 * n) ** 0.5
						return ((1 + root) / 6) % 1 == 0
def     A__      (					__lowerCAmelCase		:      int = 5000    ):
						lowerCamelCase__								=	[(i * (3 * i - 1)) // 2 for i in range(1 ,     __lowerCAmelCase    )]
						for i, pentagonal_i in enumerate(__lowerCAmelCase    ):
												for j in range(__lowerCAmelCase ,     len(__lowerCAmelCase    )    ):
																		lowerCamelCase__								=	pentagonal_nums[j]
																		lowerCamelCase__								=	pentagonal_i + pentagonal_j
																		lowerCamelCase__								=	pentagonal_j - pentagonal_i
																		if is_pentagonal(__lowerCAmelCase    ) and is_pentagonal(__lowerCAmelCase    ):
																								return b

						return -1


if __name__ == "__main__":
							print(F'{solution() = }')









"""simple docstring"""







def      UpperCamelCase       ( _A )     ->       int:
				lowercase    :      Dict       = 0
				while num > 0:
								digit_sum += num % 10
								num //= 10
				return digit_sum


def      UpperCamelCase       ( _A = 100 )     ->       int:
				lowercase    :      Union[str, Any]       = 1
				lowercase    :      Tuple       = 2

				for i in range(2  ,				max_n + 1 ):
								lowercase    :      Any       = pre_numerator
								lowercase    :      Dict       = 2 * i // 3 if i % 3 == 0 else 1
								lowercase    :      Optional[Any]       = cur_numerator
								lowercase    :      str       = e_cont * pre_numerator + temp

				return sum_digits(_A )


if __name__ == "__main__":
				print(F'{solution() = }')
