_lowercase							:      List[Any]      							={
    '''Pillow''': '''Pillow''',
    '''accelerate''': '''accelerate>=0.11.0''',
    '''compel''': '''compel==0.1.8''',
    '''black''': '''black~=23.1''',
    '''datasets''': '''datasets''',
    '''filelock''': '''filelock''',
    '''flax''': '''flax>=0.4.1''',
    '''hf-doc-builder''': '''hf-doc-builder>=0.3.0''',
    '''huggingface-hub''': '''huggingface-hub>=0.13.2''',
    '''requests-mock''': '''requests-mock==1.10.0''',
    '''importlib_metadata''': '''importlib_metadata''',
    '''invisible-watermark''': '''invisible-watermark''',
    '''isort''': '''isort>=5.5.4''',
    '''jax''': '''jax>=0.2.8,!=0.3.2''',
    '''jaxlib''': '''jaxlib>=0.1.65''',
    '''Jinja2''': '''Jinja2''',
    '''k-diffusion''': '''k-diffusion>=0.0.12''',
    '''torchsde''': '''torchsde''',
    '''note_seq''': '''note_seq''',
    '''librosa''': '''librosa''',
    '''numpy''': '''numpy''',
    '''omegaconf''': '''omegaconf''',
    '''parameterized''': '''parameterized''',
    '''protobuf''': '''protobuf>=3.20.3,<4''',
    '''pytest''': '''pytest''',
    '''pytest-timeout''': '''pytest-timeout''',
    '''pytest-xdist''': '''pytest-xdist''',
    '''ruff''': '''ruff>=0.0.241''',
    '''safetensors''': '''safetensors''',
    '''sentencepiece''': '''sentencepiece>=0.1.91,!=0.1.92''',
    '''scipy''': '''scipy''',
    '''onnx''': '''onnx''',
    '''regex''': '''regex!=2019.12.17''',
    '''requests''': '''requests''',
    '''tensorboard''': '''tensorboard''',
    '''torch''': '''torch>=1.4''',
    '''torchvision''': '''torchvision''',
    '''transformers''': '''transformers>=4.25.1''',
    '''urllib3''': '''urllib3<=2.0.0''',
}







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())






