#include<bits/stdc++.h>
#define Gc() getchar()
#define Me(x,y) memset(x,y,sizeof(x))
#define Mc(x,y) memcpy(x,y,sizeof(x))
#define d(x,y) ((m)*(x-1)+(y))
#define R(n) (rnd()%(n)+1)
#define Pc(x) putchar(x)
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define eb emplace_back
#define all(x) x.begin(),x.end()
using namespace std;using ll=long long;using db=double;using lb=long db;using ui=unsigned;using ull=unsigned long long;using pii=pair<int,int>;
const int N=1e6+5,M=5e6+5,K=1000+5,mod=998244353,Mod=mod-1;const db eps=1e-9;const int INF=1e9;mt19937 rnd(time(0));
#define Tp template<typename T>
#define Ts template<typename T,typename... Ar>
namespace Debug{
	Tp void _debug(char* f,T t){cerr<<f<<'='<<t<<endl;}
	Ts void _debug(char* f,T x,Ar... y){while(*f!=',') cerr<<*f++;cerr<<'='<<x<<",";_debug(f+1,y...);}
	#ifdef LOCAL
	#define gdb(...) _debug((char*)#__VA_ARGS__,__VA_ARGS__)
	#else 
	#define gdb(...) void()
	#endif
}using namespace Debug;
ll n;
ll calc3(ll n){
	n%=mod;
	return n*(n+1)%mod*(2*n+1)%mod*((mod+1)/6)%mod;
}
ll calc2(ll n){
	n%=mod;
	return n*(n+1)/2%mod;
}
ll sq(ll x){x%=mod;return x*x%mod;}

int pr[N],flag[N],ph;
ll w[N],sp[N];int wh,i1[N],i2[N];
ll calcp1(ll n){
	ph=0;Me(flag,0);
	for(int i=2;1ll*i*i<=n;i++){
		if(!flag[i]) pr[++ph]=i;
		for(int j=1;j<=ph&&1ll*i*i*pr[j]*pr[j]<=n;j++){
			flag[i*pr[j]]=1;
			if(i%pr[j]==0) break;
		} 
	}
	for(int i=1;i<=ph;i++) sp[i]=sp[i-1]+pr[i];
	ll x=1;
	wh=0;
	while(x<=n){
		w[++wh]=n/x;
		(w[wh]<=n/w[wh]?i1[w[wh]]:i2[n/w[wh]])=wh;
		x=n/(n/x)+1;
	}
	static ll f[N];
	for(int i=1;i<=wh;i++) f[i]=calc2(w[i])-1;
	auto getid=[&](ll x){
		return x<=n/x?i1[x]:i2[n/x];
	};
	for(int i=1;i<=ph;i++){
		for(int j=1;j<=wh&&w[j]>=1ll*pr[i]*pr[i];j++){
			f[j]=(f[j]-(f[getid(w[j]/pr[i])]-sp[i-1])%mod*pr[i])%mod;
		}
	}
	return (f[1]%mod+mod-f[2]+mod)%mod;
}
ll calcp2(ll n){
	ph=0;Me(flag,0);
	for(int i=2;1ll*i*i<=n;i++){
		if(!flag[i]) pr[++ph]=i;
		for(int j=1;j<=ph&&1ll*i*i*pr[j]*pr[j]<=n;j++){
			flag[i*pr[j]]=1;
			if(i%pr[j]==0) break;
		} 
	}
	for(int i=1;i<=ph;i++) sp[i]=(sp[i-1]+1ll*pr[i]*pr[i])%mod;
	ll x=1;
	wh=0;
	while(x<=n){
		w[++wh]=n/x;
		(w[wh]<=n/w[wh]?i1[w[wh]]:i2[n/w[wh]])=wh;
		x=n/(n/x)+1;
	}
	static ll f[N];
	for(int i=1;i<=wh;i++) f[i]=calc3(w[i])-1;
	auto getid=[&](ll x){
		return x<=n/x?i1[x]:i2[n/x];
	};
	for(int i=1;i<=ph;i++){
		for(int j=1;j<=wh&&w[j]>=1ll*pr[i]*pr[i];j++){
			f[j]=(f[j]-(f[getid(w[j]/pr[i])]-sp[i-1])%mod*pr[i]%mod*pr[i]%mod)%mod;
		}
	}
	return (f[1]%mod+mod-f[2]+mod)%mod;
}
void Solve(){
	int i,j;scanf("%lld",&n);
	ll ans=sq(calc2(n)-1);
	ans-=calc3(n)-1;
	ll tot=calcp1(n);
	ans+=calcp2(n);
	ans-=tot*(calc2(n)-tot-1)*2+tot*tot;
	printf("%lld\n",(ans%mod+mod)%mod*(mod+1>>1)%mod);
}
int main(){
	int t=1;
	// scanf("%d",&t);
	while(t--) Solve();
	cerr<<clock()*1.0/CLOCKS_PER_SEC<<'\n';
}