


from __future__ import annotations

from collections.abc import Generator
def      _a					( ):


		"""simple docstring"""




		lowercase__				= {}
		lowercase__				= 2
		while True:
				lowercase__				= factor_map.pop(SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE	)
				if factor:
						lowercase__				= factor + prime
						while x in factor_map:
								x += factor
						lowercase__				= factor
				else:
						lowercase__				= prime
						yield prime
				prime += 1
def      _a					( SCREAMING_SNAKE_CASE = 1E10	):


		"""simple docstring"""




		lowercase__				= sieve()

		lowercase__				= 1
		while True:
				lowercase__				= next(SCREAMING_SNAKE_CASE	)
				if (2 * prime * n) > limit:
						return n
				# Ignore the next prime as the reminder will be 2.
				next(SCREAMING_SNAKE_CASE	)
				n += 2


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









from __future__ import annotations

import math


def 		_SCREAMING_SNAKE_CASE     ( lowerCAmelCase__						):

		if num <= 0:
				lowerCamelCase_	:     Optional[int] 						=      F"{num}: Invalid input, please enter a positive integer."
				raise ValueError(lowerCAmelCase__						)

		lowerCamelCase_	:     str 						=      [True] * (num + 1)
		lowerCamelCase_	:     List[str] 						=      []
		lowerCamelCase_	:     Optional[int] 						=      2
		lowerCamelCase_	:     List[str] 						=      int(math.sqrt(lowerCAmelCase__						)						)

		while start <= end:
				# If start is a prime
				if sieve[start] is True:
						prime.append(lowerCAmelCase__						)

						# Set multiples of start be False
						for i in range(start * start							,num + 1							,lowerCAmelCase__						):
								if sieve[i] is True:
										lowerCamelCase_	:     Tuple 						=      False

				start += 1

		for j in range(end + 1							,num + 1						):
				if sieve[j] is True:
						prime.append(lowerCAmelCase__						)

		return prime


if __name__ == "__main__":
		print(prime_sieve(int(input("""Enter a positive integer: """).strip())))
