






from math import isqrt, loga
def 		_a       ( a					:int					)				->     list[int]:
 a						    = [True] * max_number
 for i in range(2      ,				isqrt(max_number - 1					) + 1					):
  if is_prime[i]:
   for j in range(i**2      ,				a      ,				a					):
    a						    = False

 return [i for i in range(2      ,				a					) if is_prime[i]]
def 		_a       ( a					:int = 800_800      ,				a					:int = 800_800					)				->     int:
 a						    = degree * loga(a					)
 a						    = int(a					)
 a						    = calculate_prime_numbers(a					)

 a						    = 0
 a						    = 0
 a						    = len(a					) - 1
 while left < right:
  while (
      prime_numbers[right] * loga(prime_numbers[left]					)
      + prime_numbers[left] * loga(prime_numbers[right]					)
      > upper_bound
  ):
   right -= 1
  hybrid_integers_count += right - left
  left += 1

 return hybrid_integers_count


if __name__ == "__main__":
     print(f"""{solution() = }""")










from typing import TYPE_CHECKING

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


UpperCAmelCase__							  =						{
    "configuration_rag": ["RagConfig"],
    "retrieval_rag": ["RagRetriever"],
    "tokenization_rag": ["RagTokenizer"],
}

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     UpperCAmelCase__							  =						[
         "RagModel",
         "RagPreTrainedModel",
         "RagSequenceForGeneration",
         "RagTokenForGeneration",
     ]

try:
     if not is_tf_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     UpperCAmelCase__							  =						[
         "TFRagModel",
         "TFRagPreTrainedModel",
         "TFRagSequenceForGeneration",
         "TFRagTokenForGeneration",
     ]


if TYPE_CHECKING:
     from .configuration_rag import RagConfig
     from .retrieval_rag import RagRetriever
     from .tokenization_rag import RagTokenizer

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_rag import RagModel, RagPreTrainedModel, RagSequenceForGeneration, RagTokenForGeneration

     try:
          if not is_tf_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_tf_rag import (
              TFRagModel,
              TFRagPreTrainedModel,
              TFRagSequenceForGeneration,
              TFRagTokenForGeneration,
          )

else:
     import sys

     UpperCAmelCase__							  =						_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)


