
import math







def 						_snake_case(  SCREAMING_SNAKE_CASE__    )			->   list:
       lowercase							:					Dict	     =				[True] * n
       lowercase							:					str	     =				False
       lowercase							:					int	     =				False
       lowercase							:					int	     =				True

       for i in range(3 ,     int(n**0.5 + 1    ) ,     2    ):
              lowercase							:					List[str]	     =				i * 2
              while index < n:
                     lowercase							:					Dict	     =				False
                     lowercase							:					List[str]	     =				index + i

       lowercase							:					Union[str, Any]	     =				[2]

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

       return primes







def 						_snake_case(  SCREAMING_SNAKE_CASE__ = 999_966_663_333    )			->   int:
       lowercase							:					List[Any]	     =				math.floor(math.sqrt(SCREAMING_SNAKE_CASE__    )    ) + 100
       lowercase							:					Dict	     =				prime_sieve(SCREAMING_SNAKE_CASE__    )

       lowercase							:					Optional[Any]	     =				0
       lowercase							:					Tuple	     =				0
       lowercase							:					List[str]	     =				primes[prime_index]

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

              lowercase							:					str	     =				last_prime**2
              lowercase							:					List[Any]	     =				next_prime**2

              # Get numbers divisible by lps(current)
              lowercase							:					List[str]	     =				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)
              lowercase							:					Dict	     =				upper_bound - next_prime
              while current > lower_bound:
                     matches_sum += current
                     current -= next_prime

              # Remove the numbers divisible by both ups and lps
              lowercase							:					Dict	     =				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
              lowercase							:					List[str]	     =				next_prime
              prime_index += 1

       return matches_sum


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


def 						_snake_case(  SCREAMING_SNAKE_CASE__    )			->   int:
       assert (
           isinstance(SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__    ) and number_of_steps > 0
       ), f"number_of_steps needs to be positive integer, your input {number_of_steps}"
       if number_of_steps == 1:
              return 1
       lowercase     ,      lowercase							:					Tuple	     =				1, 1
       for _ in range(number_of_steps - 1    ):
              lowercase     ,      lowercase							:					str	     =				current + previous, current
       return current


if __name__ == "__main__":
  import doctest

  doctest.testmod()
