import math
def       __magic_name__(  __UpperCAmelCase		)						->    list:



      '''simple docstring'''

      _lowerCamelCase			    =				[True] * n
      _lowerCamelCase			    =				False
      _lowerCamelCase			    =				False
      _lowerCamelCase			    =				True

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

      _lowerCamelCase			    =				[2]

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

      return primes
def       __magic_name__(  __UpperCAmelCase = 9999_6666_3333		)						->    int:



      '''simple docstring'''

      _lowerCamelCase			    =				math.floor(math.sqrt(__UpperCAmelCase		)		) + 100
      _lowerCamelCase			    =				prime_sieve(__UpperCAmelCase		)

      _lowerCamelCase			    =				0
      _lowerCamelCase			    =				0
      _lowerCamelCase			    =				primes[prime_index]

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

            _lowerCamelCase			    =				last_prime**2
            _lowerCamelCase			    =				next_prime**2

            # Get numbers divisible by lps(current)
            _lowerCamelCase			    =				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)
            _lowerCamelCase			    =				upper_bound - next_prime
            while current > lower_bound:
                  matches_sum += current
                  current -= next_prime

            # Remove the numbers divisible by both ups and lps
            _lowerCamelCase			    =				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
            _lowerCamelCase			    =				next_prime
            prime_index += 1

      return matches_sum


if __name__ == "__main__":
     print(solution())
def       __magic_name__(  __UpperCAmelCase ,						__UpperCAmelCase		)						->    bool:



      '''simple docstring'''

      _lowerCamelCase			    =				len(__UpperCAmelCase		)
      _lowerCamelCase			    =				[[False] * (required_sum + 1) for _ in range(arr_len + 1		)]

      # for each arr value, a sum of zero(0) can be formed by not taking any element
      # hence True/1
      for i in range(arr_len + 1		):
            _lowerCamelCase			    =				True

      # sum is not zero and set is empty then false
      for i in range(1 ,						required_sum + 1		):
            _lowerCamelCase			    =				False

      for i in range(1 ,						arr_len + 1		):
            for j in range(1 ,						required_sum + 1		):
                  if arr[i - 1] > j:
                        _lowerCamelCase			    =				subset[i - 1][j]
                  if arr[i - 1] <= j:
                        _lowerCamelCase			    =				subset[i - 1][j] or subset[i - 1][j - arr[i - 1]]

      return subset[arr_len][required_sum]


if __name__ == "__main__":
     import doctest

     doctest.testmod()