






from __future__ import annotations

import math



def  a__ (__lowercase							:int   )		-> list[int]:

				if num <= 0:
								_A	:				int   =      f"""{num}: Invalid input, please enter a positive integer."""
								raise ValueError(__lowercase   )

				_A	:				int   =      [True] * (num + 1)
				_A	:				Dict   =      []
				_A	:				List[str]   =      2
				_A	:				Any   =      int(math.sqrt(__lowercase   )   )

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

												# Set multiples of start be False
												for i in range(start * start					,  num + 1					,  __lowercase   ):
																if sieve[i] is True:
																				_A	:				List[Any]   =      False

								start += 1

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

				return prime


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











from __future__ import annotations



def  a__ (__lowercase							:list					,  __lowercase							:int | None = None					,  __lowercase							:int | None = None   )		-> None:
				if start is None:
								_A	:				Optional[int]   =      0

				if end is None:
								_A	:				Union[str, Any]   =      len(__lowercase   ) - 1

				if start >= end:
								return

				_A	:				Union[str, Any]   =      (start + end) // 2

				slowsort(__lowercase					,  __lowercase					,  __lowercase   )
				slowsort(__lowercase					,  mid + 1					,  __lowercase   )

				if sequence[end] < sequence[mid]:
								_A  ,				_A	:				Optional[int]   =      sequence[mid], sequence[end]

				slowsort(__lowercase					,  __lowercase					,  end - 1   )


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

	testmod()



