






from __future__ import annotations


def 				snake_case__							(							UpperCAmelCase							:  list[int]    ,			UpperCAmelCase							:  list[int]    ,			UpperCAmelCase							:  int       ):
    lowerCAmelCase__   :Dict      							=				list(range(len(UpperCAmelCase       )       )       )
    lowerCAmelCase__   :Optional[Any]      							=				[v / w for v, w in zip(UpperCAmelCase    ,			UpperCAmelCase       )]
    index.sort(key=lambda UpperCAmelCase       : ratio[i]    ,			reverse=UpperCAmelCase       )

    lowerCAmelCase__   :float      							=				0
    lowerCAmelCase__   :list[float]      							=				[0] * len(UpperCAmelCase       )
    for i in index:
        if weight[i] <= capacity:
            lowerCAmelCase__   :List[str]      							=				1
            max_value += value[i]
            capacity -= weight[i]
        else:
            lowerCAmelCase__   :List[Any]      							=				capacity / weight[i]
            max_value += value[i] * capacity / weight[i]
            break

    return max_value, fractions


if __name__ == "__main__":
 import doctest

 doctest.testmod()








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() = }""")



