#include<bits/stdc++.h>
using namespace std;

#include<atcoder/all>
using namespace atcoder;
using mint=atcoder::modint998244353;

#define int long long

struct FastFactrize{
    vector<int> SPF;
    FastFactrize(int N):SPF(N+1,1){
        for(int i=2;i<=N;i++){
            if(SPF[i]!=1)continue;
            for(int j=i;j<=N;j+=i){
                if(SPF[j]==1)SPF[j]=i;
            }
        }
    };
    
    vector<int> factrize_vector(int n){
        vector<int> ret;
        while(SPF[n]!=1){
            ret.push_back(SPF[n]);
            n/=SPF[n];
        }
        return ret;
    }

    vector<int> factrize_set(int n){
        vector<int> ret=factrize_vector(n);
        ret.erase(unique(ret.begin(),ret.end()));
        return ret;
    }

    map<int,int> factrize_map(int n){
        map<int,int> ret;
        while(SPF[n]!=1){
            ret[SPF[n]]++;
            n/=SPF[n];
        }
        return ret;
    }
    vector<int> factor(int n){
        vector<int> ret={1};
        for(auto[i,j]:factrize_map(n)){
            vector<int> nret;
            for(int e:ret){
                int x=1;
                for(int e2=0;e2<=j;e2++){
                    nret.push_back(e*x);
                    x*=i;
                }
            }
            swap(ret,nret);
        }
        return ret;
    }
};

mint op(mint a,mint b){return a*b;}
mint e(){return 1;}

signed main(){
	int n;cin>>n;

	vector<int> cnt(n+1);

	FastFactrize f(n);

	for(int i=1;i<=n;i++){
		for(auto&&e:f.factrize_vector(i)){
			cnt[e]++;
		}
	}

	vector<int> v;

	for(auto&&e:cnt){
		if(e)v.push_back(e);
	}

	segtree<mint,op,e> seg(v.size());

	vector<pair<int,int>> t;

	for(int i=0;i<v.size();i++){
		seg.set(i,v[i]+1);
		for(int j=1;j<=v[i];j++){
			t.push_back({v[i]/j,i});
		}
	}

	sort(t.begin(),t.end());

	mint ans=0;

	for(auto&&e:t){
		ans+=e.first*seg.prod(0,e.second)*seg.prod(e.second+1,v.size());
		seg.set(e.second,seg.get(e.second)-1);
	}

	cout<<ans.val()<<endl;
}