#include <bits/stdc++.h>

using namespace std;
using LL=long long;
const LL maxn=1e6+10,mod=998244353;
LL n,sq;
LL v[maxn],prime[maxn],sp1[maxn],sp2[maxn],sp3[maxn];
LL g1[maxn],g2[maxn],g3[maxn],w[maxn],id1[maxn],id2[maxn],tot;

LL qpow(LL a,LL z)
{
	LL ans=1;
	while (z){
		if (z&1) ans=ans*a%mod;
		a=a*a%mod;
		z>>=1;
	}
	return ans;
}

LL inv2=qpow(2,mod-2),inv6=qpow(6,mod-2);

void init()
{
	prime[0]=0;
	for (int i=2;i<=sq;++i){
		if (!v[i]){
			prime[++prime[0]]=i;
			int cnt=prime[0];
			sp1[cnt]=(sp1[cnt-1]+i)%mod;
			sp2[cnt]=(sp2[cnt-1]+1)%mod;
			sp3[cnt]=(sp3[cnt-1]+1ll*i*i%mod)%mod;
		}
		for (int j=1;prime[j]*i<maxn;++j){
			v[prime[j]*i]=prime[j];
			if (i%prime[j]==0) break;
		}
	}
}

LL g(LL k,LL x)
{
	return k/(k/x);
}

LL S(LL i,LL j)
{
	if (prime[j]>=i) return 0;
	LL p=i<=sq?id1[i]:id2[n/i];
	LL ans=((g1[p]+mod)%mod-(sp1[j]+mod)%mod+mod)%mod;
	
	for (int k=j+1;prime[k]*prime[k]<=i and k<=prime[0];k++){
		LL pe=prime[k];
		for (int e=1;pe<=i;e++,pe=pe*prime[k]){
			ans=(ans+(prime[k]^e)%mod*(S(i/pe,k)+(e>1))%mod)%mod;
		}
	}
	return ans;
}

int main()
{
	cin>>n;
	LL allsum=n%mod*((n+1)%mod)%mod*inv2%mod;
	allsum=(allsum-1+mod)%mod;
	LL allpls=n%mod*((n+1)%mod)%mod*((2*n+1)%mod)%mod*inv6%mod;
	allpls=(allpls-1+mod)%mod;
	sq=sqrt(n);
	init();
//	cout<<"sum(i) = "<<allsum<<'\n';
//	cout<<"sum(i^2) = "<<allpls<<'\n';
	
	
	for (LL l=1,r;l<=n;l=r+1){
		r=min(n,g(n,l));
		w[++tot]=n/l%mod;
		
		g1[tot]=(w[tot]*(w[tot]+1)%mod*inv2%mod-1+mod)%mod;
		g2[tot]=(w[tot]-1+mod)%mod;
		g3[tot]=(w[tot]*(w[tot]+1)%mod*(2*w[tot]+1)%mod*inv6%mod-1+mod)%mod;
		
		w[tot]=n/l;
		if (w[tot]<=sq) id1[w[tot]]=tot;
		else id2[n/w[tot]]=tot;
	}
	
	for (int j=1;j<=prime[0];j++){
		for (int i=1;i<=tot and prime[j]*prime[j]<=w[i];i++){
			LL tmp=w[i]/prime[j];
			LL p=tmp<=sq?id1[tmp]:id2[n/tmp];
			
			g1[i]=(g1[i]-prime[j]*(g1[p]-sp1[j-1]+mod)%mod+mod)%mod;
			g2[i]=(g2[i]-1%mod*(g2[p]-sp2[j-1]+mod)%mod+mod)%mod;
			g3[i]=(g3[i]-prime[j]*prime[j]%mod*(g3[p]-sp3[j-1]+mod)%mod+mod)%mod;
		}
	}
	LL f2=g1[1],f2p=g3[1];
//	cout<<"sum(p) = "<<f2<<'\n';
//	cout<<"sum(p^2) = "<<f2p<<'\n';
	n=n/2;
	sq=sqrt(n);
	init();
	tot=0;
	
	for (LL l=1,r;l<=n;l=r+1){
		r=min(n,g(n,l));
		w[++tot]=n/l%mod;
		
		g1[tot]=(w[tot]*(w[tot]+1)%mod*inv2%mod-1+mod)%mod;
		g2[tot]=(w[tot]-1+mod)%mod;
		g3[tot]=(w[tot]*(w[tot]+1)%mod*(2*w[tot]+1)%mod*inv6%mod-1+mod)%mod;
		
		w[tot]=n/l;
		if (w[tot]<=sq) id1[w[tot]]=tot;
		else id2[n/w[tot]]=tot;
	}
	
	for (int j=1;j<=prime[0];j++){
		for (int i=1;i<=tot and prime[j]*prime[j]<=w[i];i++){
			LL tmp=w[i]/prime[j];
			LL p=tmp<=sq?id1[tmp]:id2[n/tmp];
			
			g1[i]=(g1[i]-prime[j]*(g1[p]-sp1[j-1]+mod)%mod+mod)%mod;
			g2[i]=(g2[i]-1%mod*(g2[p]-sp2[j-1]+mod)%mod+mod)%mod;
			g3[i]=(g3[i]-prime[j]*prime[j]%mod*(g3[p]-sp3[j-1]+mod)%mod+mod)%mod;
		}
	}
//	cout<<"sum(lip) = "<<g1[1]<<'\n';
//	cout<<"sum(lip^2) = "<<g3[1]<<'\n';
	f2=(f2-g1[1]+mod)%mod;
	f2p=(f2p-g3[1]+mod)%mod;
	LL ans=(allsum-f2+mod)%mod*(allsum-f2+mod)%mod;
	ans=(ans-allpls+mod)%mod;
	ans=(ans+f2p)%mod;
	cout<<ans*inv2%mod<<'\n';	
}