




import math



def 					UpperCAmelCase__     (   lowerCamelCase      ):
  lowercase			:List[Any]							=  [True] * n
  lowercase			:int							=  False
  lowercase			:List[Any]							=  False
  lowercase			:Union[str, Any]							=  True

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

  lowercase			:List[str]							=  [2]

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

  return primes



def 					UpperCAmelCase__     (   lowerCamelCase = 999966663333      ):
  lowercase			:Tuple							=  math.floor(math.sqrt(lowerCamelCase      )      ) + 100
  lowercase			:int							=  prime_sieve(lowerCamelCase      )

  lowercase			:int							=  0
  lowercase			:str							=  0
  lowercase			:List[Any]							=  primes[prime_index]

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

    lowercase			:str							=  last_prime**2
    lowercase			:int							=  next_prime**2

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

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

  return matches_sum


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









from typing import TYPE_CHECKING

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


_UpperCAmelCase		:  int	=   {"configuration_swin": ["SWIN_PRETRAINED_CONFIG_ARCHIVE_MAP", "SwinConfig", "SwinOnnxConfig"]}


try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     _UpperCAmelCase		:  List[str]	=   [
         "SWIN_PRETRAINED_MODEL_ARCHIVE_LIST",
         "SwinForImageClassification",
         "SwinForMaskedImageModeling",
         "SwinModel",
         "SwinPreTrainedModel",
         "SwinBackbone",
     ]

try:
     if not is_tf_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     _UpperCAmelCase		:  int	=   [
         "TF_SWIN_PRETRAINED_MODEL_ARCHIVE_LIST",
         "TFSwinForImageClassification",
         "TFSwinForMaskedImageModeling",
         "TFSwinModel",
         "TFSwinPreTrainedModel",
     ]

if TYPE_CHECKING:
     from .configuration_swin import SWIN_PRETRAINED_CONFIG_ARCHIVE_MAP, SwinConfig, SwinOnnxConfig

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_swin import (
              SWIN_PRETRAINED_MODEL_ARCHIVE_LIST,
              SwinBackbone,
              SwinForImageClassification,
              SwinForMaskedImageModeling,
              SwinModel,
              SwinPreTrainedModel,
          )

     try:
          if not is_tf_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_tf_swin import (
              TF_SWIN_PRETRAINED_MODEL_ARCHIVE_LIST,
              TFSwinForImageClassification,
              TFSwinForMaskedImageModeling,
              TFSwinModel,
              TFSwinPreTrainedModel,
          )

else:
     import sys

     _UpperCAmelCase		:  int	=   _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)



