#include <iostream>
#include <algorithm>
#include <cmath>

using namespace std;

typedef long long ll;
typedef double db;

const int N = 5e5 + 7;
const ll M = 1e11;
const int Mod = 998244353;

ll Lim, lim;
ll lis[N];
int mp[N][2], cnt = 0, lpf[N], pcnt = 0, pri[N];

ll G[N][2], Fprime[N];

ll qpow(ll x, ll y)
{
    if (y < 0)
        return qpow(qpow(x, Mod - 2), -y);
    ll ret = 1;
    while (y)
    {
        if (y & 1)
            ret = ret * x % Mod;
        x = x * x % Mod, y >>= 1;
    }
    return ret;
}

const ll inv2 = qpow(2ll, Mod - 2);
const ll inv6 = qpow(6ll, Mod - 2);

inline const int Id(const ll &x)
{
    return x <= lim ? mp[x][0] : mp[Lim / x][1];
}

// inline const ll f(const ll &x)
// {
//     return x % Mod;
// }

// ll F(const ll n, const int k)
// {
//     if (n < pri[k] || n <= 1)
//         return 0;
//     ll ans = (Fprime[Id(n)] - Fprime[Id(pri[k - 1])] + Mod) % Mod;
//     for (int i = k; i <= pcnt && 1ll * pri[i] * pri[i] <= n; i++)
//         for (ll pw = pri[i]; pw <= n / pri[i]; pw *= pri[i])
//             ans = (ans + f(pw) * F(n / pw, i + 1) % Mod + f(pw * pri[i])) % Mod;
//     return ans;
// }

int main()
{
    cin >> Lim;
    pri[0] = 1;
    lim = sqrtl(Lim);
    cnt = pcnt = 0;
    for (int i = 2; i <= lim; i++)
        lpf[i] = 0;
    for (int i = 2; i <= lim; i++)
    {
        if (!lpf[i])
        {
            lpf[i] = ++pcnt;
            pri[pcnt] = i;
        }
        for (int j = 1; j <= lpf[i] && 1ll * i * pri[j] <= lim; j++)
            lpf[i * pri[j]] = j;
    }
    for (ll l = 1, r = 0, v; l <= Lim; l = r + 1)
    {
        r = Lim / (Lim / l);
        lis[++cnt] = v = Lim / l;
        (v <= lim ? mp[v][0] : mp[Lim / v][1]) = cnt;
        G[cnt][0] = (v + 2ll) % Mod * ((v - 1ll) % Mod) % Mod * inv2 % Mod;
        G[cnt][1] = v % Mod * ((v + 1) % Mod) % Mod * ((2ll * v + 1ll) % Mod) % Mod * inv6 % Mod;
        G[cnt][1] = (G[cnt][1] + Mod - 1ll) % Mod;
    }
    ll v;
    for (int k = 1; k <= pcnt; k++)
    {
        const ll pw = (ll)pri[k] * pri[k];
        for (int i = 1; pw <= lis[i]; i++)
        {
            const int id1 = Id(lis[i] / pri[k]);
            const int id2 = Id(pri[k - 1]);
            G[i][0] = (G[i][0] - pri[k] * ((G[id1][0] - G[id2][0] + Mod) % Mod) % Mod + Mod) % Mod;
            G[i][1] = (G[i][1] - 1ll * pri[k] * pri[k] % Mod * ((G[id1][1] - G[id2][1] + Mod) % Mod) % Mod + Mod) % Mod;
        }
    }
    // cout << G[1][0] - G[2][0] << "\n";
    // cout << G[1][1] - G[2][1] << "\n";
    ll x1 = (G[1][0] - G[2][0] + Mod) % Mod;
    ll x2 = (G[1][1] - G[2][1] + Mod) % Mod;
    ll ans1 = (2ll + Lim) % Mod * ((Lim - 1) % Mod) % Mod * inv2 % Mod;
    ans1 = (ans1 + Mod - x1) % Mod;
    ans1 = ans1 * ans1 % Mod;
    ll ans2 = Lim % Mod * ((Lim + 1) % Mod) % Mod * ((2ll * Lim + 1ll) % Mod) % Mod * inv6 % Mod;
    ans2 = (ans2 + Mod - 1 - x2) % Mod;
    ll ans = (ans1 - ans2 + Mod) % Mod * inv2 % Mod;
    cout << ans;
}