


"""simple docstring"""






import math







def        lowerCamelCase_(		_lowerCamelCase       )    ->     list:
   '''simple docstring'''





   _lowerCamelCase   :				List[str]							=     [True] * n
   _lowerCamelCase   :				Optional[int]							=     False
   _lowerCamelCase   :				List[str]							=     False
   _lowerCamelCase   :				str							=     True

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

   _lowerCamelCase   :				Optional[int]							=     [2]

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

   return primes







def        lowerCamelCase_(		_lowerCamelCase = 999966663333       )    ->     int:
   '''simple docstring'''





   _lowerCamelCase   :				Optional[Any]							=     math.floor(math.sqrt(_lowerCamelCase       )       ) + 100
   _lowerCamelCase   :				str							=     prime_sieve(_lowerCamelCase       )

   _lowerCamelCase   :				Dict							=     0
   _lowerCamelCase   :				List[str]							=     0
   _lowerCamelCase   :				Optional[Any]							=     primes[prime_index]

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

      _lowerCamelCase   :				Dict							=     last_prime**2
      _lowerCamelCase   :				Dict							=     next_prime**2

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

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

   return matches_sum


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



"""simple docstring"""




from typing import TYPE_CHECKING

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


__magic_name__						: Any    =				{'configuration_glpn': ['GLPN_PRETRAINED_CONFIG_ARCHIVE_MAP', 'GLPNConfig']}

try:
					if not is_vision_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					__magic_name__						: Dict    =				['GLPNFeatureExtractor']
					__magic_name__						: Union[str, Any]    =				['GLPNImageProcessor']

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					__magic_name__						: int    =				[
					    'GLPN_PRETRAINED_MODEL_ARCHIVE_LIST',
					    'GLPNForDepthEstimation',
					    'GLPNLayer',
					    'GLPNModel',
					    'GLPNPreTrainedModel',
					]


if TYPE_CHECKING:
					from .configuration_glpn import GLPN_PRETRAINED_CONFIG_ARCHIVE_MAP, GLPNConfig

					try:
										if not is_vision_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .feature_extraction_glpn import GLPNFeatureExtractor
										from .image_processing_glpn import GLPNImageProcessor

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_glpn import (
										    GLPN_PRETRAINED_MODEL_ARCHIVE_LIST,
										    GLPNForDepthEstimation,
										    GLPNLayer,
										    GLPNModel,
										    GLPNPreTrainedModel,
										)


else:
					import sys

					__magic_name__						: Optional[int]    =				_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




