




'''simple docstring'''


def 						snake_case_       (UpperCamelCase			:    int ):





							'''simple docstring'''


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

							_a      	=							[True] * (num + 1)

							_a      	=							2
							while p * p <= num:
														if primes[p]:
																					for i in range(p * p					,		num + 1					,		UpperCamelCase ):
																												_a      	=							False
														p += 1

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


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				_snake_case : Optional[Any]  				=						int(input('Enter a positive integer: ').strip())
				print(prime_sieve_eratosthenes(user_num))







'''simple docstring'''


from math import pi, sqrt
def 						snake_case_       (UpperCamelCase			:    float ):





							'''simple docstring'''


							if num <= 0:
														raise ValueError('''math domain error''' )
							if num > 171.5:
														raise OverflowError('''math range error''' )
							elif num - int(UpperCamelCase ) not in (0, 0.5):
														raise NotImplementedError('''num must be an integer or a half-integer''' )
							elif num == 0.5:
														return sqrt(UpperCamelCase )
							else:
														return 1.0 if num == 1 else (num - 1) * gamma(num - 1 )
def 						snake_case_       ():





							'''simple docstring'''


							assert gamma(0.5 ) == sqrt(UpperCamelCase )
							assert gamma(1 ) == 1.0
							assert gamma(2 ) == 1.0


if __name__ == "__main__":
				from doctest import testmod

				testmod()
				_snake_case : Optional[Any]  				=						1.0
				while num:
								_snake_case : Dict  				=						float(input('Gamma of: '))
								print(F'''gamma({num}) = {gamma(num)}''')
								print('\nEnter 0 to exit...')

