



'''simple docstring'''





import math




def lowerCAmelCase    (__A):



     """simple docstring"""



     _a           =    [True] * n
     _a           =    False
     _a           =    False
     _a           =    True

     for i in range(3    ,      int(n**0.5 + 1)    ,      2):
          _a           =    i * 2
          while index < n:
               _a           =    False
               _a           =    index + i

     _a           =    [2]

     for i in range(3    ,      __A    ,      2):
          if is_prime[i]:
               primes.append(__A)

     return primes




def lowerCAmelCase    (__A = 999_966_663_333):



     """simple docstring"""



     _a           =    math.floor(math.sqrt(__A)) + 100
     _a           =    prime_sieve(__A)

     _a           =    0
     _a           =    0
     _a           =    primes[prime_index]

     while (last_prime**2) <= limit:
          _a           =    primes[prime_index + 1]

          _a           =    last_prime**2
          _a           =    next_prime**2

          # Get numbers divisible by lps(current)
          _a           =    lower_bound + last_prime
          while upper_bound > current <= limit:
               matches_sum += current
               current += last_prime

          # Reset the upper_bound
          while (upper_bound - next_prime) > limit:
               upper_bound -= next_prime

          # Add the numbers divisible by ups(current)
          _a           =    upper_bound - next_prime
          while current > lower_bound:
               matches_sum += current
               current -= next_prime

          # Remove the numbers divisible by both ups and lps
          _a           =    0
          while upper_bound > current <= limit:
               if current <= lower_bound:
                    # Increment the current number
                    current += last_prime * next_prime
                    continue

               if current > limit:
                    break

               # Remove twice since it was added by both ups and lps
               matches_sum -= current * 2

               # Increment the current number
               current += last_prime * next_prime

          # Setup for next pair
          _a           =    next_prime
          prime_index += 1

     return matches_sum


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





from math import isqrt





def      lowerCamelCase_					(							lowerCamelCase__       ):
				lowerCamelCase_         =     [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__       ):
																lowerCamelCase_         =     False

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





def      lowerCamelCase_					(							lowerCamelCase__ = 1_0**8       ):
				lowerCamelCase_         =     calculate_prime_numbers(max_number // 2       )

				lowerCamelCase_         =     0
				lowerCamelCase_         =     0
				lowerCamelCase_         =     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() = }""")


