"""simple docstring"""






from math import ceil, sqrt


def     UpperCAmelCase__ (       lowerCAmelCase__  :int = 1_0_0_0_0_0_0	)				->					int:
      '''simple docstring'''


      lowercase														=			0

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




"""simple docstring"""






from __future__ import annotations

import math


def     UpperCAmelCase__ (       lowerCAmelCase__  :int	)				->					list[int]:
      '''simple docstring'''


      if num <= 0:
            lowercase														=			f'{num}: Invalid input, please enter a positive integer.'
            raise ValueError(lowerCAmelCase__	)

      lowercase														=			[True] * (num + 1)
      lowercase														=			[]
      lowercase														=			2
      lowercase														=			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:
                              lowercase														=			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())))



