#include<iostream>
#include<algorithm>
#include<stack>
#include<set>
#include<unordered_set>
#include<queue>
#include<deque>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<map>
#include<string>
#include<vector>
#include<array>
#include<functional>
#define int long long
using namespace std;
typedef long long ll;
ll highbit(ll x){
    ll ans=2;
    int num=1;
    while(x){
        x>>=2;
        ans<<=2;
        num++;
    }
    return num;
}
ll lowbit(ll x){
    return x&(-x);
}
long long max(long long a,long long b){
    return a>b?a:b;
}
long long min(long long a,long long b){
    return a>b?b:a;
}
ll gcd(ll x,ll y)
{
    if(y==1)
        return x;
    return gcd(y,x%y);
}
const int N = 1000010;
const ll mod=998244353;
const ll in2=499122177,in6=166374059;
ll md(ll x){
    return x%mod;
}
struct MIN1{
    ll prime[N], id1[N], id2[N], flag[N], ncnt, m;
    ll g[N], sum[N], a[N], T;
    ll n;
    ll ID(ll x) {
        return x <= T ? id1[x] : id2[n / x];
    }
    ll calc(ll x) {
        x%=mod;
        return ((md(x * md(x + 1) )%mod)*in2%mod + mod - 1)%mod;
    }
    ll f(ll x) {
        return md(x);
    }
    ll init(ll n){
        T = sqrt(n+0.5);
        for (int i = 2; i <= T; i++) {
            if (!flag[i]) prime[++ncnt] = i, sum[ncnt] = md(sum[ncnt - 1] + i),sum[ncnt]=md(sum[ncnt]);
            
            for (int j = 1; j <= ncnt && i * prime[j] <= T; j++) {
                flag[i * prime[j]] = 1;
                if (i % prime[j] == 0) break;
            }
        }
        for (ll l = 1; l <= n; l = n / (n / l) + 1) {
            a[++m] = n / l;
            if (a[m] <= T) id1[a[m]] = m; else id2[n / a[m]] = m;
            g[m] = calc(a[m]);
        }
        for (ll i = 1; i <= ncnt; i++)
            for (ll j = 1; j <= m && (ll)prime[i] * prime[i] <= a[j]; j++){
                g[j] = g[j] 
                - ((ll)prime[i] * ((g[ID(a[j] / prime[i])] - sum[i - 1]+mod)%mod))%mod;
                g[j]%=mod;
                g[j]=(g[j]+mod)%mod;
            }

        return 0;
    }
    ll solve(ll x){
        if(x<=1){return x;}
        return n=x,init(n),g[ID(n)];
    }
}m11,m12;

struct MIN2{
    ll prime[N], id1[N], id2[N], flag[N], ncnt, m;
    ll g[N], sum[N], a[N], T;
    ll n;
    ll ID(ll x) {
        return x <= T ? id1[x] : id2[n / x];
    }
    ll calc(ll x) {
        return md(md(md((md(x)*md(x+1))%mod)*md(md(2*x+1)))*in6%mod-1+mod);
    }
    ll f(ll x) {
        return x;
    }
    ll init(ll n){
        T = sqrt(n + 0.5);
        for (int i = 2; i <= T; i++) {
            if (!flag[i]) prime[++ncnt] = i, sum[ncnt] = sum[ncnt - 1] + md(i*i),sum[ncnt]=md(sum[ncnt]);
            for (int j = 1; j <= ncnt && i * prime[j] <= T; j++) {
                flag[i * prime[j]] = 1;
                if (i % prime[j] == 0) break;
            }
        }
        for (ll l = 1; l <= n; l = n / (n / l) + 1) {
            a[++m] = n / l;
            if (a[m] <= T) id1[a[m]] = m; else id2[n / a[m]] = m;
            g[m] = calc(a[m]);
        }
        for (ll i = 1; i <= ncnt; i++)
            for (ll j = 1; j <= m && prime[i] * prime[i] <= a[j]; j++){
                g[j] = g[j] - 
                md(md(prime[i]*prime[i]) * md(g[ID(a[j] / prime[i])] - sum[i - 1])),g[j]=(g[j]%mod+mod)%mod;
                g[j]%=mod;
                g[j]=(g[j]+mod)%mod;
            }
        return 0;
    }
    ll solve(ll x){
        if(x<=1){return x;}
        return n=x,init(n),g[ID(n)];
    }
}m21,m22;
signed main(void){
    unsigned int t;
    //freopen("input.in","r",stdin);
    ll n;
    cin>>n;
    ll pre1=m11.solve(n)-m12.solve((n+1)/2);
    ll pre2=m21.solve(n)-m22.solve((n+1)/2);
    pre1=md(md(pre1)+mod);
    pre2=md(md(pre2)+mod);
    ll ans=0;
    ll k=n%mod;
    ll buff=md(md(md((2+k)*(k-1))*in2)*md(md((2+k)*(k-1))*in2));
    buff-=md(md(md(k*md(k+1))*md(2*k+1))*in6);
    buff=md(md(buff)+mod);
    buff++;
    buff*=in2;
    buff%=mod;
    ans=md( md(md(md((2+k)*(k-1))*in2)*pre1)-pre2-md(md((pre1*pre1)-pre2)*in2)+mod );
    ans=(buff-ans+mod)%mod;
    cout<<ans<<endl;
    return 0;
}