
"""simple docstring"""






def __A						(   a_ :							int     )->							list[int]:




		'''simple docstring'''






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

		SCREAMING_SNAKE_CASE       :     Optional[int]				= [True] * (num + 1)

		SCREAMING_SNAKE_CASE       :     Optional[Any]				= 2
		while p * p <= num:
				if primes[p]:
						for i in range(p * p		,		num + 1		,		a_     ):
								SCREAMING_SNAKE_CASE       :     Any				= False
				p += 1

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


if __name__ == "__main__":
					import doctest

					doctest.testmod()

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







"""simple docstring"""






from __future__ import annotations

from fractions import Fraction





def __A						(   a_ :							int		,		a_ :							int     )->							bool:




		'''simple docstring'''






		return (
		    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
		)





def __A						(   a_ :							int     )->							list[str]:




		'''simple docstring'''






		SCREAMING_SNAKE_CASE       :     Union[str, Any]				= []
		SCREAMING_SNAKE_CASE       :     List[str]				= 11
		SCREAMING_SNAKE_CASE       :     Union[str, Any]				= int('''1''' + '''0''' * digit_len     )
		for num in range(a_		,		a_     ):
				while den <= 99:
						if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
								if is_digit_cancelling(a_		,		a_     ):
										solutions.append(F"{num}/{den}"     )
						den += 1
				num += 1
				SCREAMING_SNAKE_CASE       :     Optional[Any]				= 10
		return solutions





def __A						(   a_ :							int = 2     )->							int:




		'''simple docstring'''






		SCREAMING_SNAKE_CASE       :     Optional[Any]				= 1.0
		for fraction in fraction_list(a_     ):
				SCREAMING_SNAKE_CASE       :     List[str]				= Fraction(a_     )
				result *= frac.denominator / frac.numerator
		return int(a_     )


if __name__ == "__main__":
					print(solution())





