#include<bits/stdc++.h>
using namespace std;
using ll=long long;
const int N=4e5;
const int mod=998244353,iv6=166374059;
int add(int x,int y){ return (x+=y)>=mod?x-mod:x; }
int sub(int x,int y){ return (x-=y)<0?x+mod:x; }
bool p[N+5];
int np[N+5],ps;
int sp1[N+5],sp2[N+5];
void prep(){
    p[0]=p[1]=1;
    for(int i=2;i<=N;i++)
        if(!p[i]){
            np[++ps]=i;
            for(int j=i*2;j<=N;j+=i) p[j]=1;
        }
    for(int i=1;i<=ps;i++){
        sp1[i]=add(np[i],sp1[i-1]);
        sp2[i]=(sp2[i-1]+1ll*np[i]*np[i])%mod;
    }
}
ll n;
int tot;
ll R[N*2+5],g1[N*2+5],g2[N*2+5];
int id[N*2+5];
int gid(ll x){
    return x<=N?id[x]:id[N+n/x];
}
int S1(ll x){
    x%=mod;
    return 1ll*x*(x+1)/2%mod;
}
int S2(ll x){
    x%=mod;
    return 1ll*x*(x+1)%mod*(2*x+1)%mod*iv6%mod;
}
int main(){
    prep();
    scanf("%lld",&n);
    for(ll l=1,r;l<=n;l=r+1){
        r=n/(n/l);
        R[++tot]=r;
        if(r<=N) id[r]=tot;
        else id[n/r+N]=tot;
    }
    for(int i=1;i<=tot;i++){
        g1[i]=sub(S1(R[i]),1);
        g2[i]=sub(S2(R[i]),1);
    }
    for(int i=1;i<=ps&&1ll*np[i]*np[i]<=n;i++){
        int p2=1ll*np[i]*np[i]%mod;
        for(int j=tot;R[j]>=1ll*np[i]*np[i];j--){
            int k=gid(R[j]/np[i]);
            g1[j]=(g1[j]+1ll*(mod-np[i])*(g1[k]-sp1[i-1]+mod))%mod;
            g2[j]=(g2[j]+1ll*(mod-p2)*(g2[k]-sp2[i-1]+mod))%mod;
        }
    }
    int res1=sub(g1[tot],g1[tot-1]);
    int res2=sub(g2[tot],g2[tot-1]);
    int ans=(S1(n)-1-res1)%mod;
    ans=1ll*ans*ans%mod;
    ans=(0ll+ans-S2(n)+1+res2)%mod;
    ans=1ll*ans*(mod+1)/2%mod;
    printf("%d\n",(ans+mod)%mod);
    return 0;
}