#include<bits/stdc++.h>
#define ll long long
#define lll __int128
using namespace std;
const int N=1e6+5,M=1e7+5,mod=998244353;
ll cc,sq,cnt,p[M],f[N],tot,w[N],g[N],sum1[N],sum2[N];
int id1[N],id2[N];
bool vis[M];
ll quick_pow(ll x,ll y)
{
	ll res=1;x%=mod;
	for(;y;y>>=1)
	{
		if(y&1) res=res*x%mod;
		x=x*x%mod;
	}
	return res;
}

ll inv(ll x){
	return quick_pow(x,mod-2);
} 
void shai(ll x)
{
	cc=0;
	for(int i=2;i<=x;i++)
	{
		if(!vis[i]) p[++cc]=i,(sum1[cc]=sum1[cc-1]+i)%mod,sum2[cc]=(sum2[cc-1]+1ll*i*i%mod)%mod;
		for(int j=1;j<=cc&&p[j]*i<=x;j++)
		{
			vis[i*p[j]]=true;
			if(!(i%p[j])) break;
		}
	}
	return;
}
void init(ll x,ll n)
{
	tot=0;
	cnt=upper_bound(p+1,p+cc+1,x)-p-1;
	for(ll l=1,r;l<=n;l=r+1)
	{
		r=(n/(n/l));
		w[++tot]=n/l;
		if(n/l<=x) id1[n/l]=tot;
		else id2[n/(n/l)]=tot;
	}
	return;
}
ll n,m,t,o;
int id(ll x) {return x<=sq?id1[x]:id2[o/x];} 
void calc_sum()
{
	for(int i=1;i<=tot;i++) g[i]=((1ll*(1+w[i])%mod*(w[i]%mod))%mod*inv(2)%mod+mod-1)%mod;
	for(int i=1;i<=cnt;i++)
		for(int j=1;j<=tot;j++)
			{
				if(p[i]*p[i]>w[j]) break;
				g[j]-=(g[id(w[j]/p[i])]-sum1[i-1])*p[i]%mod;
				g[j]%=mod;
				g[j]=(g[j]+mod)%mod;
			}
	return;
}
void calc_sum2()
{
	for(int i=1;i<=tot;i++) g[i]=((w[i]%mod)*(w[i]%mod+1)%mod*(w[i]%mod*2+1)%mod*inv(6)%mod+mod-1)%mod;
	for(int i=1;i<=cnt;i++)
		for(int j=1;j<=tot;j++)
			{
				if(p[i]*p[i]>w[j]) break;
				g[j]-=(g[id(w[j]/p[i])]-sum2[i-1])*p[i]%mod*p[i]%mod;
				g[j]%=mod;
				g[j]=(g[j]+mod)%mod;
			}
	return;
}
ll get_sum(ll x)
{
	sq=sqrt(x);
	init(sq,x);
	o=x;
	calc_sum();
	return g[1];
}
ll get_sum2(ll x)
{
	sq=sqrt(x);
	init(sq,x);
	o=x;
	calc_sum2();
	return g[1];
}

ll g_sum(ll x){
	x%=mod;
	return (x*(x+1)%mod*inv(2) - 1 + mod)%mod;
}

ll g_sum2(ll x){
	x%=mod;
	return (x*(x+1)%mod*(2*x+1)%mod*inv(6)-1 + mod)%mod;
}
int main()
{
//	freopen("E.in","r",stdin);
//	freopen("E+.out","w",stdout);
	std::ios::sync_with_stdio(false);
	cin.tie(0); 
	cout.tie(0);
	cin>>n;
	shai(M-1);
	ll a1 = (mod + get_sum(n) - get_sum(n/2))%mod;
	ll a2 = (mod + get_sum2(n) - get_sum2(n/2))%mod;
	ll a3 = g_sum(n);
	ll a4 = g_sum2(n); 
	ll ans = (a3 * a3%mod - a4 + mod)*inv(2) %mod;
	ans = (ans - a1 * (a3 - a1)%mod + mod )%mod;
	ll a5 = (a1 * a1 %mod - a2 +mod)*inv(2)%mod;
	ans = (ans - a5 + mod)%mod;
	if(ans<0)ans+=mod;
	cout<<ans; 
    return 0;
}