
"""simple docstring"""




from math import isqrt



def 							a__ (				lowerCAmelCase	:       int		):






     '''simple docstring'''
     UpperCAmelCase__							: Tuple 							=						[True] * max_number
     for i in range(2       ,    isqrt(max_number - 1		) + 1		):
          if is_prime[i]:
               for j in range(i**2       ,    lowerCAmelCase       ,    lowerCAmelCase		):
                    UpperCAmelCase__							: List[Any] 							=						False

     return [i for i in range(2       ,    lowerCAmelCase		) if is_prime[i]]



def 							a__ (				lowerCAmelCase	:       int = 10**8		):






     '''simple docstring'''
     UpperCAmelCase__							: Dict 							=						calculate_prime_numbers(max_number // 2		)

     UpperCAmelCase__							: Optional[int] 							=						0
     UpperCAmelCase__							: Optional[int] 							=						0
     UpperCAmelCase__							: Tuple 							=						len(lowerCAmelCase		) - 1
     while left <= right:
          while prime_numbers[left] * prime_numbers[right] >= max_number:
               right -= 1
          semiprimes_count += right - left + 1
          left += 1

     return semiprimes_count


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





"""simple docstring"""




def 							a__ (				lowerCAmelCase	:       int		):






     '''simple docstring'''
     if a < 0:
          raise ValueError("Input value must be a positive integer"		)
     elif isinstance(lowerCAmelCase       ,    lowerCAmelCase		):
          raise TypeError("Input value must be a 'int' type"		)
     return bin(lowerCAmelCase		).count("1"		)


if __name__ == "__main__":
    import doctest

    doctest.testmod()



