NOD

const int MX = 1e6+123;
bitset<MX> is_prime;
vector<int> prime;

void primeGen ( int n )
{
    n += 100;
    for ( int i = 3; i <= n; i += 2 ) is_prime[i] = 1;

    int sq = sqrt ( n );
    for ( int i = 3; i <= sq; i += 2 ) {
        if ( is_prime[i] == 1 ) {
            for ( int j = i*i; j <= n; j += ( i + i ) ) {
                is_prime[j] = 0;
            }
        }
    }

    is_prime[2] = 1;
    prime.push_back (2);

    for ( int i = 3; i <= n; i += 2 ) {
        if ( is_prime[i] == 1 ) prime.push_back ( i );
    }
}


int NOD (long long n) // 60
{
    int ret = 1;
    for ( auto p : prime ) { // p = 5
        if ( 1LL * p * p > n ) break;

        if ( n % p == 0 ) {
            int cnt = 1;

            while ( n % p == 0 ) { // n = 5
                n /= p; // n = 5;
                cnt++; // 2
            }

            ret *= cnt; // 1 * 3 * 2
        }
    }

    if ( n > 1 ) ret *= 2; // 1 * 3 * 2  * 2 = 12

    return ret;
}