//#pragma GCC optimize ("Ofast")
//#pragma GCC optimize ("unroll-loops")
#include <bits/stdc++.h>
using namespace std;

#define int long long
#define fi first
#define se second
typedef pair<int, int> pii;
typedef long long ll;
typedef long double ld;
//mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());

const int mod = 998244353;
const int N = 1e6  + 5;

int fpow(int a, int b) {
    int res = 1;
    for (; b; b >>= 1, a = a * 1ll * a % mod) if (b & 1) res = res * 1ll * a % mod;
    return res;
}
int sum(int x) {
    static int i2 = (mod + 1) >> 1;
    return x * 1ll * (x + 1) % mod * i2 % mod;
}
int sum2(int x) {
    static int i6 = fpow(6, mod - 2);
    return x * 1ll * (x + 1) % mod * (x + x + 1) % mod * i6 % mod;
}
int sum3(int x) {
    static int i2 = (mod + 1) >> 1;
    int r = x * 1ll * (x + 1) % mod * i2 % mod;
    return r * 1ll * r % mod;
} 
int sum3(int l, int r) {
    return (sum3(r) + mod - sum3(l - 1)) % mod;
}
int sum2(int l, int r) {
    return (sum2(r) + mod - sum2(l - 1)) % mod;
}
namespace Min25 {
    int g1[N], g2[N], g3[N];
    int id1[N], id2[N], w[N], tot, sqr;
    int vis[N], pcnt, p[N], sup[N], sup2[N], sup3[N];
    void init(int n) {
        pcnt = 0;
        for (int i = 2; i <= n; i++) {
            if (!vis[i]){
                p[++pcnt] = i;
                sup[pcnt] = (sup[pcnt - 1] + i) % mod;
                sup2[pcnt] = (sup2[pcnt - 1] + i * 1ll * i % mod) % mod;
                sup3[pcnt] = (sup3[pcnt - 1] + i * 1ll * i % mod * i % mod) % mod;
            }
            for (int j = 1; j <= pcnt && p[j] * 1ll * i <= n; ++j) {
                int v = p[j] * i;
                vis[v] = 1;
                if (i % p[j] == 0) break;
            }
        }
    }
    void solve(ll n) {
        tot = 0;
        int sqr = sqrt(n + 0.5) + 1;
        init(sqr);
        for (ll i = 1, j; i <= n; i = j + 1) {
            j = n / (n / i);
            w[++tot] = n / i;
            g1[tot] = (sum(w[tot] % mod) + mod - 1) % mod;
            g2[tot] = (sum2(w[tot] % mod) + mod - 1) % mod;
            g3[tot] = (sum3(w[tot] % mod) + mod - 1) % mod;
            if (w[tot] <= sqr) id1[w[tot]] = tot;
            else id2[j] = tot;
        }
        for (int j = 1; j <= pcnt; j++) {
            for (int i = 1; i <= tot && p[j] * p[j] <= w[i]; i++) {
                ll t = w[i] / p[j];
                int k;
                if (t <= sqr) k = id1[t];
                else k = id2[n / t];
                g1[i] += (mod - p[j] * ((g1[k] + mod - sup[j - 1]) % mod) % mod) % mod;
                g1[i] %= mod;
                g2[i] += (mod - p[j] * p[j] % mod * ((g2[k] + mod - sup2[j - 1]) % mod) % mod) % mod;
                g2[i] %= mod;
            }
        }
    }
}
int check(int x) {
    for (int i = 2; i * i <= x; i++) if (x % i == 0) return false;
    return true;
}
void MAIN() {
    ll n;
    cin >> n;
    const int i2 = (mod + 1) >> 1;
    ll res = sum3(2, n % mod) * 1ll * i2 % mod;
    res = (res + mod - sum2(2, n % mod) * 1ll * i2 % mod) % mod;
    res = (res + mod - (sum(n % mod) + mod - 1) % mod) % mod;
    Min25::solve(n);
    int HS = (sum(n % mod) + mod - 1 - Min25::g1[1]) % mod;
    int SS = (sum(n % mod) + mod - 1) % mod;
    //cout << HS << ' ' << Min25::g1[1] << '\n';
    int S1 = Min25::g1[1];
    int S2 = Min25::g2[1];
    Min25::solve(n / 2);
    HS = (HS + Min25::g1[1]) % mod;
    S2 = (S2 + mod - Min25::g2[1]) % mod;
    S1 = (S1 + mod - Min25::g1[1]) % mod;
    int t = (S1 * SS % mod + S1 * HS % mod + mod - S2) % mod * i2 % mod;
    cout << (res + mod - t) % mod << '\n';
}

signed main() {
#ifdef LOCAL
    auto start = chrono::steady_clock::now();
    freopen("miku.in", "r", stdin);
    freopen("miku.out", "w", stdout);
#endif
    ios::sync_with_stdio(0); cin.tie(0);
    int T = 1;
    // cin >> T;
    while (T--) MAIN();
#ifdef LOCAL
    auto end = chrono::steady_clock::now();
    cout << "\nqwq: " <<  chrono::duration_cast<chrono::milliseconds>(end - start).count() << "ms\n";
#endif
    return 0;
}