
'''simple docstring'''






import math







def 		A_       (	_lowerCAmelCase   :    int							):



      """simple docstring"""




      _lowerCamelCase				:   List[str]								=   [True] * n
      _lowerCamelCase				:   Dict								=   False
      _lowerCamelCase				:   Any								=   False
      _lowerCamelCase				:   int								=   True

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

      _lowerCamelCase				:   int								=   [2]

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

      return primes







def 		A_       (	_lowerCAmelCase   :    int = 999966663333							):



      """simple docstring"""




      _lowerCamelCase				:   Union[str, Any]								=   math.floor(math.sqrt(_lowerCAmelCase							)							) + 100
      _lowerCamelCase				:   Union[str, Any]								=   prime_sieve(_lowerCAmelCase							)

      _lowerCamelCase				:   List[str]								=   0
      _lowerCamelCase				:   List[Any]								=   0
      _lowerCamelCase				:   Any								=   primes[prime_index]

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

            _lowerCamelCase				:   int								=   last_prime**2
            _lowerCamelCase				:   Optional[int]								=   next_prime**2

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

            # Remove the numbers divisible by both ups and lps
            _lowerCamelCase				:   List[Any]								=   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				:   Optional[Any]								=   next_prime
            prime_index += 1

      return matches_sum


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

'''simple docstring'''






import warnings

from ..trainer import Trainer
from ..utils import logging


UpperCAmelCase_       :   Union[str, Any]   =       logging.get_logger(__name__)

class  UpperCAmelCase__						(       A ):



    def __init__(	self      :       int,__A      :       Any=None,**__A      :       Optional[Any]     ):
          warnings.warn(
              "`SageMakerTrainer` is deprecated and will be removed in v5 of Transformers. You can use `Trainer` "
              "instead.",__A,)
          super().__init__(args=__A,**__A     )