




from math import ceil, sqrt


def 						lowerCamelCase__    (		_A = 1000000							):







	'''simple docstring'''





	snake_case_		    =     0

	for outer_width in range(3     ,	(limit // 4) + 2							):
		if outer_width**2 > limit:
			snake_case_		    =     max(ceil(sqrt(outer_width**2 - limit							)							)     ,	1							)
		else:
			snake_case_		    =     1
		if (outer_width - hole_width_lower_bound) % 2:
			hole_width_lower_bound += 1

		answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

	return answer


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))
