




def 						lowerCamelCase__    (		_A = 10**12							):







	'''simple docstring'''





	snake_case_		    =     1
	snake_case_		    =     0

	snake_case_		    =     1
	snake_case_		    =     1

	while numerator <= 2 * min_total - 1:
		prev_numerator += 2 * numerator
		numerator += 2 * prev_numerator

		prev_denominator += 2 * denominator
		denominator += 2 * prev_denominator

	return (denominator + 1) // 2


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






def 						lowerCamelCase__    (		_A							):







	'''simple docstring'''





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

	snake_case_		    =     [True] * (num + 1)

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

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


if __name__ == "__main__":
		import doctest

		doctest.testmod()

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