#include <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <cmath>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
#include <complex>
#include <unordered_map>
#include <unordered_set>
#include <random>
#include <cassert>
#include <fstream>
#include <utility>
#include <functional>
#include <time.h>
#include <stack>
#include <array>
#define popcount __builtin_popcount
using namespace std;
typedef long long int ll;
typedef pair<int, int> P;
const ll MOD=998244353;
const int MAX=1000010;
bitset<MAX> isprime;
void sieve(){
    for(int i=3; i<MAX; i++, i++) isprime[i]=1;
    isprime[2]=1;
    for(int i=3; i<MAX; i++){
        if(isprime[i]){
            for(int j=(i<<1); j<MAX; j+=i) isprime[j]=0;
        }
    }
}
int main()
{
	ll n; cin>>n;
	if(n==1){
	    cout<<8<<endl;
	    return 0;
	}
    sieve();
	ll sq=1;
	while((sq+1)*(sq+1)<=n) sq++;
	vector<vector<int>> vd(sq+1);
	vector<int> m(sq+1, 1);
	for(int d=1; d<=sq; d++){
	    if(!isprime[d]) continue;
	    for(int i=d; i<=sq; i+=d){
	        if(i/d%d==0) m[i]=0;
	        m[i]=-m[i];
	    }
	}
	ll x1=sq, ans=56;
	ll x[1000010];
	for(ll i=2; i<=sq; i++){
	    while(x1*x1>n-i*i) x1--;
	    x[i]=min(x1, i);
	}
	for(int d=1; d<=sq; d++){
        for(int i=d; i<=sq; i+=d){
            if(i==1) continue;
            ll y=x[i]/d;
            ll s=(((y*(y+1))>>1)*d%MOD+y*i)*48%MOD;
            if(m[d]==1) ans+=s;
	        else if(m[d]==-1) ans+=MOD-s;
	        if(ans>=MOD) ans-=MOD;
        }
    }
	cout<<ans<<endl;
	return 0;
}