#include<bits/stdc++.h>
using namespace std;
#define int long long

const int MOD = 998244353, inv2 = (MOD+1)/2, inv3 = (MOD+1)/3, inv6 = (MOD+1)/6;
void inc(int &x, int a){if ((x+=a)>=MOD) x-=MOD;}
void dec(int &x, int a){if ((x-=a)<0) x+=MOD;}
void mul(int &x, int a){x=1LL*x*a%MOD;}

namespace Min25 {

const int $N = 1e6+5;
bool isp[$N]; int pri[$N], totp;
int sp1[$N], g1[$N];
int sp2[$N], g2[$N];
int $n, Sqr, tot, w[$N], ind1[$N], ind2[$N];

void initPri(int n) {
    isp[1] = 1;
    for (int i=1; i<=n; ++i) {
        if (!isp[i]) {
            pri[++totp] = i;
            sp1[totp] = (sp1[totp-1] + i)%MOD;
            sp2[totp] = (sp2[totp-1] + 1LL*i*i)%MOD;
        }
        for (int j=1; j<=totp&&pri[j]*i<=n; ++j) {
            isp[i*pri[j]] = 1;
            if (i%pri[j]==0) break;
        }
    }
}

void initMin25(int n) {
    tot = 0;
    $n = n;
    Sqr = sqrtl(n);
    initPri(Sqr);
    for (int i=1; i<=n; ) {
        int j = n/(n/i);
        w[++tot] = n/i;
        g1[tot] = w[tot]%MOD;
        g2[tot] = g1[tot]*(g1[tot]+1)/2%MOD*(2*g1[tot]+1)%MOD*inv3%MOD;
        g1[tot] = g1[tot]*(g1[tot]+1)/2%MOD;
        dec(g2[tot], 1); dec(g1[tot], 1);
        if (n/i<=Sqr) ind1[n/i]=tot;
        else ind2[n/(n/i)]=tot;
        i=j+1;
    }

    for (int i=1; i<=totp; ++i) {
        for (int j=1; j<=tot&&pri[i]*pri[i]<=w[j]; ++j) {
            int k = w[j]/pri[i]<=Sqr ? ind1[w[j]/pri[i]] : ind2[n/(w[j]/pri[i])];
            dec(g1[j], pri[i]*(g1[k]-sp1[i-1]+MOD)%MOD);
            dec(g2[j], pri[i]*pri[i]%MOD*(g2[k]-sp2[i-1]+MOD)%MOD);
        }
    }
}

}using namespace Min25;



signed main() {
    ios::sync_with_stdio(0); cin.tie(0);
    int n; cin >> n; int nn=n%MOD;
    int sum=(nn+2)*(nn-1)%MOD*inv2%MOD;

    initMin25(n);
    int sp=(g1[1]%MOD-g1[2]%MOD+MOD)%MOD,sp2=(g2[1]%MOD-g2[2]%MOD+MOD)%MOD;

    // initMin25(n/2);
    // sp=(sp-g1[1]%MOD+MOD)%MOD;
    // sp2=(sp2-g2[1]%MOD+MOD)%MOD;

    int ans=(sum*sum%MOD-(nn*(n+1)%MOD*(2*nn+1)%MOD*inv6%MOD-1+MOD)%MOD+MOD)%MOD*inv2%MOD;
    ans=(ans-sp*sum%MOD+sp2+MOD)%MOD;
    ans=(ans+(sp*sp%MOD-sp2+MOD)%MOD*inv2%MOD)%MOD;
    cout<<ans<<endl;
    // printf("tot=%lld g0=%lld g1=%lld\n", tot, g1[1], g2[1]);
    // printf("w:"); for (int i=1; i<=tot; ++i) printf("%lld ", w[i]); puts("");
    // printf("g1:"); for (int i=1; i<=tot; ++i) printf("%lld ", g1[i]); puts("");
    return 0;
}