
"""simple docstring"""




from ..utils import DummyObject, requires_backends



class 	lowerCAmelCase_						(metaclass=a__  ):


				"""simple docstring"""



				__UpperCamelCase      :						Optional[int]					       =   ['''torch''', '''torchsde''']



				def __init__(self   ,       *SCREAMING_SNAKE_CASE__   ,       **SCREAMING_SNAKE_CASE__    )					->		Any:



											"""simple docstring"""




											requires_backends(self   ,       ["""torch""", """torchsde"""]    )



				@classmethod
				def 	__magic_name__    (cls   ,       *SCREAMING_SNAKE_CASE__   ,       **SCREAMING_SNAKE_CASE__    )					->		Union[str, Any]:



											"""simple docstring"""




											requires_backends(cls   ,       ["""torch""", """torchsde"""]    )



				@classmethod
				def 	__magic_name__    (cls   ,       *SCREAMING_SNAKE_CASE__   ,       **SCREAMING_SNAKE_CASE__    )					->		str:



											"""simple docstring"""




											requires_backends(cls   ,       ["""torch""", """torchsde"""]    )









"""simple docstring"""
from math import isqrt, loga

def       _snake_case						(						UpperCamelCase						:		int						):
 UpperCAmelCase	:					Any	=	[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						):
    UpperCAmelCase	:					str	=	False

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

def       _snake_case						(						UpperCamelCase						:		int = 800800			,		UpperCamelCase						:		int = 800800						):
 UpperCAmelCase	:					Union[str, Any]	=	degree * loga(UpperCamelCase						)
 UpperCAmelCase	:					int	=	int(UpperCamelCase						)
 UpperCAmelCase	:					Union[str, Any]	=	calculate_prime_numbers(UpperCamelCase						)

 UpperCAmelCase	:					Dict	=	0
 UpperCAmelCase	:					Optional[int]	=	0
 UpperCAmelCase	:					Dict	=	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() = }""")
