from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


_lowercase							:      str      							={
    '''configuration_mvp''': ['''MVP_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''MvpConfig''', '''MvpOnnxConfig'''],
    '''tokenization_mvp''': ['''MvpTokenizer'''],
}

try:
				if not is_tokenizers_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				_lowercase							:      Dict      							=['''MvpTokenizerFast''']

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				_lowercase							:      Any      							=[
				    '''MVP_PRETRAINED_MODEL_ARCHIVE_LIST''',
				    '''MvpForCausalLM''',
				    '''MvpForConditionalGeneration''',
				    '''MvpForQuestionAnswering''',
				    '''MvpForSequenceClassification''',
				    '''MvpModel''',
				    '''MvpPreTrainedModel''',
				]

if TYPE_CHECKING:
				from .configuration_mvp import MVP_PRETRAINED_CONFIG_ARCHIVE_MAP, MvpConfig, MvpOnnxConfig
				from .tokenization_mvp import MvpTokenizer

				try:
								if not is_tokenizers_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .tokenization_mvp_fast import MvpTokenizerFast

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_mvp import (
								    MVP_PRETRAINED_MODEL_ARCHIVE_LIST,
								    MvpForCausalLM,
								    MvpForConditionalGeneration,
								    MvpForQuestionAnswering,
								    MvpForSequenceClassification,
								    MvpModel,
								    MvpPreTrainedModel,
								)

else:
				import sys

				_lowercase							:      Dict      							=_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)







import math



def A__  (			lowercase:     int					)				->		list:
       A						:     Optional[Any]         =[True] * n
       A						:     Tuple         =False
       A						:     List[Any]         =False
       A						:     Dict         =True

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

       A						:     Tuple         =[2]

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

       return primes



def A__  (			lowercase:     int = 999_966_663_333					)				->		int:
       A						:     Optional[int]         =math.floor(math.sqrt(lowercase					)					) + 100
       A						:     Optional[int]         =prime_sieve(lowercase					)

       A						:     Optional[Any]         =0
       A						:     List[Any]         =0
       A						:     Union[str, Any]         =primes[prime_index]

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

              A						:     Optional[int]         =last_prime**2
              A						:     Tuple         =next_prime**2

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

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

       return matches_sum


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






