






from math import isqrt, loga


def 				snake_case__							(							UpperCAmelCase							:  int       ):
    lowerCAmelCase__   :Union[str, 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__       ):
                lowerCAmelCase__   :List[str]      							=				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__   :List[str]      							=				degree * loga(UpperCAmelCase__       )
    lowerCAmelCase__   :List[Any]      							=				int(UpperCAmelCase__       )
    lowerCAmelCase__   :Tuple      							=				calculate_prime_numbers(UpperCAmelCase__       )

    lowerCAmelCase__   :Union[str, Any]      							=				0
    lowerCAmelCase__   :Optional[Any]      							=				0
    lowerCAmelCase__   :int      							=				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() = }""")














import re


def 				snake_case__							(							UpperCAmelCase							:  str       ):
    return [char.split() for char in re.split(R"[^ a-z A-Z 0-9 \s]"    ,			str_       )]


def 				snake_case__							(							UpperCAmelCase							:  str       ):
    lowerCAmelCase__   :List[Any]      							=				split_input(str_       )
    return "".join(
        ["".join([char.capitalize() for char in sub_str]       ) for sub_str in string_split]       )


def 				snake_case__							(							UpperCAmelCase							:  str    ,			UpperCAmelCase							:  bool    ,			UpperCAmelCase							:  str       ):
    try:
        lowerCAmelCase__   :Dict      							=				split_input(UpperCAmelCase       )
        if upper:
            lowerCAmelCase__   :Dict      							=				"".join(
                [
                    separator.join([char.upper() for char in sub_str]       )
                    for sub_str in string_split
                ]       )
        else:
            lowerCAmelCase__   :Any      							=				"".join(
                [
                    separator.join([char.lower() for char in sub_str]       )
                    for sub_str in string_split
                ]       )
        return res_str
    except IndexError:
        return "not valid string"


def 				snake_case__							(							UpperCAmelCase							:  str       ):
    return to_simple_case(UpperCAmelCase       )


def 				snake_case__							(							UpperCAmelCase							:  str       ):
    try:
        lowerCAmelCase__   :Any      							=				to_simple_case(UpperCAmelCase       )
        return res_str[0].lower() + res_str[1:]
    except IndexError:
        return "not valid string"


def 				snake_case__							(							UpperCAmelCase							:  str    ,			UpperCAmelCase							:  bool       ):
    return to_complex_case(UpperCAmelCase    ,			UpperCAmelCase    ,			"_"       )


def 				snake_case__							(							UpperCAmelCase							:  str    ,			UpperCAmelCase							:  bool       ):
    return to_complex_case(UpperCAmelCase    ,			UpperCAmelCase    ,			"-"       )


if __name__ == "__main__":
 __import__("""doctest""").testmod()



