





"""simple docstring"""






from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


A 			=  {
    '''configuration_jukebox''': [
        '''JUKEBOX_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''JukeboxConfig''',
        '''JukeboxPriorConfig''',
        '''JukeboxVQVAEConfig''',
    ],
    '''tokenization_jukebox''': ['''JukeboxTokenizer'''],
}

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  A 			=  [
      '''JUKEBOX_PRETRAINED_MODEL_ARCHIVE_LIST''',
      '''JukeboxModel''',
      '''JukeboxPreTrainedModel''',
      '''JukeboxVQVAE''',
      '''JukeboxPrior''',
  ]

if TYPE_CHECKING:
  from .configuration_jukebox import (
      JUKEBOX_PRETRAINED_CONFIG_ARCHIVE_MAP,
      JukeboxConfig,
      JukeboxPriorConfig,
      JukeboxVQVAEConfig,
  )
  from .tokenization_jukebox import JukeboxTokenizer

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_jukebox import (
        JUKEBOX_PRETRAINED_MODEL_ARCHIVE_LIST,
        JukeboxModel,
        JukeboxPreTrainedModel,
        JukeboxPrior,
        JukeboxVQVAE,
    )

else:
  import sys

  A 			=  _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)






"""simple docstring"""






from math import isqrt, loga

def     __A      (			a_						:int)		->		list[int]:
				__a :						int			       =  [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 :						int			       =  False

				return [i for i in range(2   ,       a_) if is_prime[i]]

def     __A      (			a_						:int = 80_08_00   ,       a_						:int = 80_08_00)		->		int:
				__a :						str			       =  degree * loga(a_)
				__a :						Tuple			       =  int(a_)
				__a :						int			       =  calculate_prime_numbers(a_)

				__a :						List[Any]			       =  0
				__a :						Optional[Any]			       =  0
				__a :						Dict			       =  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() = }')