





from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


__lowerCamelCase	:					Union[str, Any]			  =					{
    """configuration_xlm_roberta_xl""": [
        """XLM_ROBERTA_XL_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """XLMRobertaXLConfig""",
        """XLMRobertaXLOnnxConfig""",
    ],
}

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    __lowerCamelCase	:					Optional[int]			  =					[
        """XLM_ROBERTA_XL_PRETRAINED_MODEL_ARCHIVE_LIST""",
        """XLMRobertaXLForCausalLM""",
        """XLMRobertaXLForMaskedLM""",
        """XLMRobertaXLForMultipleChoice""",
        """XLMRobertaXLForQuestionAnswering""",
        """XLMRobertaXLForSequenceClassification""",
        """XLMRobertaXLForTokenClassification""",
        """XLMRobertaXLModel""",
        """XLMRobertaXLPreTrainedModel""",
    ]

if TYPE_CHECKING:
    from .configuration_xlm_roberta_xl import (
        XLM_ROBERTA_XL_PRETRAINED_CONFIG_ARCHIVE_MAP,
        XLMRobertaXLConfig,
        XLMRobertaXLOnnxConfig,
    )

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_xlm_roberta_xl import (
            XLM_ROBERTA_XL_PRETRAINED_MODEL_ARCHIVE_LIST,
            XLMRobertaXLForCausalLM,
            XLMRobertaXLForMaskedLM,
            XLMRobertaXLForMultipleChoice,
            XLMRobertaXLForQuestionAnswering,
            XLMRobertaXLForSequenceClassification,
            XLMRobertaXLForTokenClassification,
            XLMRobertaXLModel,
            XLMRobertaXLPreTrainedModel,
        )

else:
    import sys

    __lowerCamelCase	:					Union[str, Any]			  =					_LazyModule(__name__, globals()["""__file__"""], _import_structure)







import math



def 		A_    (					_lowerCAmelCase					)						->			list:
 UpperCamelCase     : str	     =       [True] * n
 UpperCamelCase     : Optional[int]	     =       False
 UpperCamelCase     : str	     =       False
 UpperCamelCase     : List[Any]	     =       True

 for i in range(3							,       int(n**0.5 + 1					)							,       2					):
  UpperCamelCase     : int	     =       i * 2
  while index < n:
   UpperCamelCase     : Optional[Any]	     =       False
   UpperCamelCase     : Optional[Any]	     =       index + i

 UpperCamelCase     : Optional[Any]	     =       [2]

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

 return primes



def 		A_    (					_lowerCAmelCase = 9999_6666_3333					)						->			int:
 UpperCamelCase     : Tuple	     =       math.floor(math.sqrt(_lowerCAmelCase					)					) + 100
 UpperCamelCase     : Dict	     =       prime_sieve(_lowerCAmelCase					)

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

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

  UpperCamelCase     : Any	     =       last_prime**2
  UpperCamelCase     : Union[str, Any]	     =       next_prime**2

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

  # Remove the numbers divisible by both ups and lps
  UpperCamelCase     : 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
  UpperCamelCase     : str	     =       next_prime
  prime_index += 1

 return matches_sum


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