



from math import isqrt, loga



def 		lowerCAmelCase__    (					UpperCamelCase_				:       List[Any]	)->  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 ,       lowerCAmelCase_ ,       lowerCAmelCase_	):
																A__		 =					False

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



def 		lowerCAmelCase__    (					UpperCamelCase_				:       Union[str, Any] = 8_0_0_8_0_0 ,       UpperCamelCase_				:       Union[str, Any] = 8_0_0_8_0_0	)->  int:
				A__		 =					degree * loga(lowerCAmelCase_	)
				A__		 =					int(lowerCAmelCase_	)
				A__		 =					calculate_prime_numbers(lowerCAmelCase_	)

				A__		 =					0
				A__		 =					0
				A__		 =					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() = }")





import numpy as np



def 		lowerCAmelCase__    (					UpperCamelCase_				:       np.array	)->  np.array:
    return 1 / (1 + np.exp(-vector	))



def 		lowerCAmelCase__    (					UpperCamelCase_				:       np.array	)->  np.array:
    return vector * sigmoid(1.702 * vector	)


if __name__ == "__main__":
   import doctest

   doctest.testmod()
