






from typing import TYPE_CHECKING

# rely on isort to merge the imports
from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_a    :   Optional[Any]        =			{
    "configuration_autoformer": [
        "AUTOFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "AutoformerConfig",
    ],
}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _a    :   int        =			[
     "AUTOFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
     "AutoformerForPrediction",
     "AutoformerModel",
     "AutoformerPreTrainedModel",
 ]


if TYPE_CHECKING:
 from .configuration_autoformer import (
     AUTOFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
     AutoformerConfig,
 )

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_autoformer import (
      AUTOFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
      AutoformerForPrediction,
      AutoformerModel,
      AutoformerPreTrainedModel,
  )

else:
 import sys

 _a    :   List[Any]        =			_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)








from math import isqrt, loga


def 				snake_case__							(							UpperCAmelCase							:  int       ):
    lowerCAmelCase__   :Optional[int]      							=				[True] * max_number
    for i in range(2    ,			isqrt(max_number - 1       ) + 1       ):
        if is_prime[i]:
            for j in range(i**2    ,			UpperCAmelCase    ,			UpperCAmelCase       ):
                lowerCAmelCase__   :int      							=				False

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


def 				snake_case__							(							UpperCAmelCase							:  int = 8_0_0_8_0_0    ,			UpperCAmelCase							:  int = 8_0_0_8_0_0       ):
    lowerCAmelCase__   :str      							=				degree * loga(UpperCAmelCase       )
    lowerCAmelCase__   :Any      							=				int(UpperCAmelCase       )
    lowerCAmelCase__   :List[Any]      							=				calculate_prime_numbers(UpperCAmelCase       )

    lowerCAmelCase__   :List[str]      							=				0
    lowerCAmelCase__   :List[str]      							=				0
    lowerCAmelCase__   :Optional[Any]      							=				len(UpperCAmelCase       ) - 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() = }""")



