




"""simple docstring"""






def   _snake_case    (       lowercase__	):

				if num <= 0:
								raise ValueError('Input must be a positive integer'	)

				_lowerCamelCase  :    List[Any]					=					[True] * (num + 1)

				_lowerCamelCase  :    Dict					=					2
				while p * p <= num:
								if primes[p]:
												for i in range(p * p							,					num + 1							,					lowercase__	):
																_lowerCamelCase  :    Union[str, Any]					=					False
								p += 1

				return [prime for prime in range(2							,					num + 1	) if primes[prime]]


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			lowercase__  		=		int(input("""Enter a positive integer: """).strip())
			print(prime_sieve_eratosthenes(user_num))





"""simple docstring"""






def   _snake_case    (       lowercase__ = 1000	):
				_lowerCamelCase,				_lowerCamelCase  :    Optional[int]					=					1, 1
				_lowerCamelCase  :    int					=					[]
				for i in range(1							,					n + 1	):
								_lowerCamelCase  :    Tuple					=					prev_numerator + 2 * prev_denominator
								_lowerCamelCase  :    str					=					prev_numerator + prev_denominator
								if len(str(lowercase__	)	) > len(str(lowercase__	)	):
												result.append(lowercase__	)
								_lowerCamelCase  :    Dict					=					numerator
								_lowerCamelCase  :    Optional[int]					=					denominator

				return len(lowercase__	)


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