






'''simple docstring'''



from math import isqrt, loga


def 							lowercase_				(    __A :       int			)       ->      list[int]:



 """simple docstring"""




 lowercase					:   Dict				  =[True] * max_number
 for i in range(2					,      isqrt(max_number - 1			) + 1			):
  if is_prime[i]:
   for j in range(i**2					,      lowerCAmelCase__					,      lowerCAmelCase__			):
    lowercase					:   List[str]				  =False

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


def 							lowercase_				(    __A :       int = 8_0_0_8_0_0					,      __A :       int = 8_0_0_8_0_0			)       ->      int:



 """simple docstring"""




 lowercase					:   Dict				  =degree * loga(lowerCAmelCase__			)
 lowercase					:   Any				  =int(lowerCAmelCase__			)
 lowercase					:   List[Any]				  =calculate_prime_numbers(lowerCAmelCase__			)

 lowercase					:   List[Any]				  =0
 lowercase					:   str				  =0
 lowercase					:   Tuple				  =len(lowerCAmelCase__			) - 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() = }""")











'''simple docstring'''



import importlib.metadata
from typing import Union

from packaging.version import Version, parse

from .constants import STR_OPERATION_TO_FUNC


SCREAMING_SNAKE_CASE						=	parse(importlib.metadata.version('torch'))


def 							lowercase_				(    __A :       Union[str, Version]					,      __A :       str					,      __A :       str			)       ->      Union[str, Any]:



 """simple docstring"""




 if operation not in STR_OPERATION_TO_FUNC.keys():
  raise ValueError(F'`operation` must be one of {list(STR_OPERATION_TO_FUNC.keys()			)}, received {operation}'			)
 lowercase					:   Any				  =STR_OPERATION_TO_FUNC[operation]
 if isinstance(__A					,      __A			):
  lowercase					:   List[Any]				  =parse(importlib.metadata.version(__A			)			)
 return operation(__A					,      parse(__A			)			)





def 							lowercase_				(    __A :       str					,      __A :       str			)       ->      Tuple:



 """simple docstring"""




 return compare_versions(__A					,      __A					,      __A			)



