vector<int> get_phi(int n) {
    vector<bool> not_prime(n + 1);
    vector<int> res;
    vector<int> phi(n + 1);
    phi[1] = 1;
    for (int i = 2; i <= n; ++i) {
        if (not not_prime[i]) {
            res.emplace_back(i);
            phi[i] = i - 1;
        }
        for (auto&& x : res) {
            if (i * x > n) break;
            not_prime[i * x] = 1;
            if (i % x == 0) {
                // phi(n) = n * prod((p - 1) / p)
                // => phi(i * x) = i * x * prod((p - 1) / p) = (i * prod((p - 1) / p)) * x = phi(i) * x,
                // since `i` covers all factors of i * x
                phi[i * x] = phi[i] * x;
                break;
            } else {
                // i coprimes x
                // phi(i * x) = phi(i) * phi(x) = phi(i) * (x - 1)
                phi[i * x] = phi[i] * (x - 1);
            }
        }
    }
    return phi;
}