



def 					__snake_case     (      _UpperCAmelCase = 1000000    ):
    __a							=    set(range(3       ,			_UpperCAmelCase       ,			2    )    )
    primes.add(2    )
    for p in range(3       ,			_UpperCAmelCase       ,			2    ):
        if p not in primes:
            continue
        primes.difference_update(set(range(p * p       ,			_UpperCAmelCase       ,			_UpperCAmelCase    )    )    )

    __a							=    [float(_UpperCAmelCase    ) for n in range(limit + 1    )]

    for p in primes:
        for n in range(_UpperCAmelCase       ,			limit + 1       ,			_UpperCAmelCase    ):
            phi[n] *= 1 - 1 / p

    return int(sum(phi[2:]    )    )


if __name__ == "__main__":
 print(f'{solution() = }')










def 					__snake_case     (      _UpperCAmelCase       ,			_UpperCAmelCase    ):

    def get_matched_characters(_UpperCAmelCase       ,			_UpperCAmelCase    ) -> str:
        __a							=    []
        __a							=    min(len(_stra    )       ,			len(_stra    )    ) // 2
        for i, l in enumerate(_stra    ):
            __a							=    int(max(0       ,			i - limit    )    )
            __a							=    int(min(i + limit + 1       ,			len(_stra    )    )    )
            if l in _stra[left:right]:
                matched.append(_UpperCAmelCase    )
                __a							=    f'{_stra[0:_stra.index(_UpperCAmelCase    )]} {_stra[_stra.index(_UpperCAmelCase    ) + 1:]}'

        return "".join(_UpperCAmelCase    )

    # matching characters
    __a							=    get_matched_characters(_UpperCAmelCase       ,			_UpperCAmelCase    )
    __a							=    get_matched_characters(_UpperCAmelCase       ,			_UpperCAmelCase    )
    __a							=    len(_UpperCAmelCase    )

    # transposition
    __a							=    (
        len([(ca, ca) for ca, ca in zip(_UpperCAmelCase       ,			_UpperCAmelCase    ) if ca != ca]    ) // 2
    )

    if not match_count:
        __a							=    0.0
    else:
        __a							=    (
            1
            / 3
            * (
                match_count / len(_UpperCAmelCase    )
                + match_count / len(_UpperCAmelCase    )
                + (match_count - transpositions) / match_count
            )
        )

    # common prefix up to 4 characters
    __a							=    0
    for ca, ca in zip(stra[:4]       ,			stra[:4]    ):
        if ca == ca:
            prefix_len += 1
        else:
            break

    return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 print(jaro_winkler('''hello''', '''world'''))





