#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll mod=998244353;
const ll Ny2=(mod+1)/2; 
const ll Ny6=166374059;
typedef long double lf;
ll Mod(ll x){
    long double z=(lf)x/mod;
    x-=(ll)z*mod;
    return x;
}
const int maxn=1e6+10;
ll pr[maxn],prs[maxn],prs2[maxn],cnt=0,f[maxn];
void add(ll &x,ll y){
    if((x+=y)>=mod)x-=mod;
}
void del(ll &x,ll y){
    if((x-=y)<0)x+=mod;
}
ll Sum(ll x){
    x=Mod(x);
    return Mod(Mod(x*(x+1))*Ny2);
}
map<pair<ll,int>,ll> ma,ma2;
ll S(ll x,int m){
    while(pr[m]*pr[m]>x)m--;
    if(m==0)return Mod(Sum(x)-1+mod);
    if(ma.find({x,m})!=ma.end())return ma[{x,m}];
    ll res=Mod(Sum(x)-1+mod);
    for(int i=1;i<=m;i++){
        del(res,Mod(pr[i]*(Mod(S(x/pr[i],i-1)-prs[i-1]+mod))));

    }
    return ma[{x,m}]=res;
}
ll Sum2(ll x){
    x%=mod;
    return Mod(Mod(Mod(x*(x+1))*(2*x+1))*Ny6);
}
ll S2(ll x,int m){
    while(pr[m]*pr[m]>x)m--;
    if(m==0)return Mod(Sum2(x)-1+mod);
    if(ma2.find({x,m})!=ma2.end())return ma2[{x,m}];
    ll res=Mod(Sum2(x)-1+mod);
    for(int i=1;i<=m;i++){
        del(res,Mod(Mod(pr[i]*pr[i])*(Mod(S2(x/pr[i],i-1)-prs2[i-1]+mod))));
    }
    return ma2[{x,m}]=res;
}
signed main()
{
    for(ll i=2;i<maxn;i++)if(!f[i]){
        cnt++;pr[cnt]=i;
        prs[cnt]=Mod(prs[cnt-1]+i);
        prs2[cnt]=Mod(prs2[cnt-1]+i*i%mod);
        for(int j=i+i;j<maxn;j+=i)f[j]=1;
    }
    cnt--;
    ll n;cin>>n;
    ll p1=(S(n,cnt)-S(n/2,cnt)+mod)%mod;
    ll p2=(S2(n,cnt)-S2(n/2,cnt)+mod)%mod;
    ll z=(Sum(n)-1)*(Sum(n)-1)%mod;
    // cout<<"z="<<z<<" p1="<<p1<<" p2="<<p2<<endl;
    z=(z-(Sum(n)-1)*p1%mod-(Sum(n)-1-p1)*p1%mod+2*mod)%mod;
    // cout<<"z="<<z<<endl;
    z=(z+p2)%mod;
    z=(z-(Sum2(n)-1)+mod)%mod;
    z=z*Ny2%mod;
    cout<<z;
    // ll ans=0;
}