





def _a (  SCREAMING_SNAKE_CASE__      :  int       )	->    int:

							'''simple docstring'''






							assert isinstance(SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__       ), f'''The input value of [n={number}] is not an integer'''

							if number == 1:
														return 2
							elif number < 1:
														SCREAMING_SNAKE_CASE__       :      Optional[Any]     =						f'''The input value of [n={number}] has to be > 0'''
														raise ValueError(SCREAMING_SNAKE_CASE__       )
							else:
														SCREAMING_SNAKE_CASE__       :      Optional[int]     =						sylvester(number - 1       )
														SCREAMING_SNAKE_CASE__       :      List[Any]     =						num - 1
														SCREAMING_SNAKE_CASE__       :      Tuple     =						num
														return lower * upper + 1


if __name__ == "__main__":
		print(f"The 8th number in Sylvester's sequence: {sylvester(8)}")













def _a (  SCREAMING_SNAKE_CASE__      :  int = 50_00_00_00       )	->    int:

							'''simple docstring'''






							SCREAMING_SNAKE_CASE__       :      str     =						set()
							SCREAMING_SNAKE_CASE__       :      Dict     =						int((limit - 24) ** (1 / 2)       )

							SCREAMING_SNAKE_CASE__       :      Any     =						set(range(3			,				prime_square_limit + 1			,				2       )       )
							primes.add(2       )
							for p in range(3			,				prime_square_limit + 1			,				2       ):
														if p not in primes:
																					continue
														primes.difference_update(set(range(p * p			,				prime_square_limit + 1			,				SCREAMING_SNAKE_CASE__       )       )       )

							for primea in primes:
														SCREAMING_SNAKE_CASE__       :      Optional[int]     =						primea * primea
														for primea in primes:
																					SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						primea * primea * primea
																					if square + cube >= limit - 16:
																												break
																					for primea in primes:
																												SCREAMING_SNAKE_CASE__       :      List[str]     =						primea * primea * primea * primea
																												SCREAMING_SNAKE_CASE__       :      Optional[int]     =						square + cube + tetr
																												if total >= limit:
																																			break
																												ret.add(SCREAMING_SNAKE_CASE__       )

							return len(SCREAMING_SNAKE_CASE__       )


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






