





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


__lowerCamelCase	:					List[str]			  =					{
    'configuration_lxmert': ['LXMERT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'LxmertConfig'],
    'tokenization_lxmert': ['LxmertTokenizer'],
}

try:
    if not is_tokenizers_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    __lowerCamelCase	:					int			  =					['LxmertTokenizerFast']

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    __lowerCamelCase	:					Union[str, Any]			  =					[
        'LxmertEncoder',
        'LxmertForPreTraining',
        'LxmertForQuestionAnswering',
        'LxmertModel',
        'LxmertPreTrainedModel',
        'LxmertVisualFeatureEncoder',
        'LxmertXLayer',
    ]

try:
    if not is_tf_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    __lowerCamelCase	:					List[Any]			  =					[
        'TF_LXMERT_PRETRAINED_MODEL_ARCHIVE_LIST',
        'TFLxmertForPreTraining',
        'TFLxmertMainLayer',
        'TFLxmertModel',
        'TFLxmertPreTrainedModel',
        'TFLxmertVisualFeatureEncoder',
    ]


if TYPE_CHECKING:
    from .configuration_lxmert import LXMERT_PRETRAINED_CONFIG_ARCHIVE_MAP, LxmertConfig
    from .tokenization_lxmert import LxmertTokenizer

    try:
        if not is_tokenizers_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .tokenization_lxmert_fast import LxmertTokenizerFast

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_lxmert import (
            LxmertEncoder,
            LxmertForPreTraining,
            LxmertForQuestionAnswering,
            LxmertModel,
            LxmertPreTrainedModel,
            LxmertVisualFeatureEncoder,
            LxmertXLayer,
        )

    try:
        if not is_tf_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_tf_lxmert import (
            TF_LXMERT_PRETRAINED_MODEL_ARCHIVE_LIST,
            TFLxmertForPreTraining,
            TFLxmertMainLayer,
            TFLxmertModel,
            TFLxmertPreTrainedModel,
            TFLxmertVisualFeatureEncoder,
        )

else:
    import sys

    __lowerCamelCase	:					List[str]			  =					_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)







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())
