pair<vector<int>, vector<int>> factcount(int n) {
    vector<bool> not_prime(n + 1);
    vector<int> res(n + 1), num(n + 1);
    vector<int> primes;
    res[1] = 1;
    for (int i = 2; i <= n; ++i) {
        if (not not_prime[i]) {
            res[i] = 2;
            num[i] = 1;
            primes.emplace_back(i);
        }
        for (auto&& x : primes) {
            if (i * x > n) break;
            not_prime[i * x] = 1;
            if (i % x == 0) {
                num[i * x] = num[i] + 1;
                res[i * x] = res[i] / num[i * x] * (num[i * x] + 1);
                break;
            }
            num[i * x] = 1;
            res[i * x] = res[i] * 2;
        }
    }
    return {primes, res};
}