#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
#define rep(i,n) for(int i=0;i<int(n);i++)
#define rep1(i,n) for(int i=1;i<=int(n);i++)
#define per(i,n) for(int i=int(n)-1;i>=0;i--)
#define per1(i,n) for(int i=int(n);i>0;i--)
#define all(c) c.begin(),c.end()
#define si(x) int(x.size())
#define pb push_back
#define eb emplace_back
#define fs first
#define sc second
template<class T> using V = vector<T>;
template<class T> using VV = vector<vector<T>>;
template<class T,class U> bool chmax(T& x, U y){
	if(x<y){ x=y; return true; }
	return false;
}
template<class T,class U> bool chmin(T& x, U y){
	if(y<x){ x=y; return true; }
	return false;
}
template<class T> void mkuni(V<T>& v){sort(all(v));v.erase(unique(all(v)),v.end());}
template<class T> int lwb(const V<T>& v, const T& a){return lower_bound(all(v),a) - v.begin();}
template<class T>
V<T> Vec(size_t a) {
    return V<T>(a);
}
template<class T, class... Ts>
auto Vec(size_t a, Ts... ts) {
  return V<decltype(Vec<T>(ts...))>(a, Vec<T>(ts...));
}
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){
	return o<<"("<<p.fs<<","<<p.sc<<")";
}
template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){
	o<<"{";
	for(const T& v:vc) o<<v<<",";
	o<<"}";
	return o;
}
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); }

#ifdef LOCAL
#define show(x) cerr << "LINE" << __LINE__ << " : " << #x << " = " << (x) << endl
void dmpr(ostream& os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ~ ";
	dmpr(os,args...);
}
#define shows(...) cerr << "LINE" << __LINE__ << " : ";dmpr(cerr,##__VA_ARGS__)
#define dump(x) cerr << "LINE" << __LINE__ << " : " << #x << " = {";  \
	for(auto v: x) cerr << v << ","; cerr << "}" << endl;
#else
#define show(x) void(0)
#define dump(x) void(0)
#define shows(...) void(0)
#endif

template<class D> D divFloor(D a, D b){
	return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0);
}
template<class D> D divCeil(D a, D b) {
	return a / b + (((a ^ b) > 0 && a % b != 0) ? 1 : 0);
}
template<unsigned int mod_>
struct ModInt{
	using uint = unsigned int;
	using ll = long long;
	using ull = unsigned long long;

	constexpr static uint mod = mod_;

	uint v;
	ModInt():v(0){}
	ModInt(ll _v):v(normS(_v%mod+mod)){}
	explicit operator bool() const {return v!=0;}
	static uint normS(const uint &x){return (x<mod)?x:x-mod;}		// [0 , 2*mod-1] -> [0 , mod-1]
	static ModInt make(const uint &x){ModInt m; m.v=x; return m;}
	ModInt operator+(const ModInt& b) const { return make(normS(v+b.v));}
	ModInt operator-(const ModInt& b) const { return make(normS(v+mod-b.v));}
	ModInt operator-() const { return make(normS(mod-v)); }
	ModInt operator*(const ModInt& b) const { return make((ull)v*b.v%mod);}
	ModInt operator/(const ModInt& b) const { return *this*b.inv();}
	ModInt& operator+=(const ModInt& b){ return *this=*this+b;}
	ModInt& operator-=(const ModInt& b){ return *this=*this-b;}
	ModInt& operator*=(const ModInt& b){ return *this=*this*b;}
	ModInt& operator/=(const ModInt& b){ return *this=*this/b;}
	ModInt& operator++(int){ return *this=*this+1;}
	ModInt& operator--(int){ return *this=*this-1;}
	template<class T> friend ModInt operator+(T a, const ModInt& b){ return (ModInt(a) += b);}
	template<class T> friend ModInt operator-(T a, const ModInt& b){ return (ModInt(a) -= b);}
	template<class T> friend ModInt operator*(T a, const ModInt& b){ return (ModInt(a) *= b);}
	template<class T> friend ModInt operator/(T a, const ModInt& b){ return (ModInt(a) /= b);}
	ModInt pow(ll p) const {
		if(p<0) return inv().pow(-p);
		ModInt a = 1;
		ModInt x = *this;
		while(p){
			if(p&1) a *= x;
			x *= x;
			p >>= 1;
		}
		return a;
	}
	ModInt inv() const {		// should be prime
		return pow(mod-2);
	}
	// ll extgcd(ll a,ll b,ll &x,ll &y) const{
	// 	ll p[]={a,1,0},q[]={b,0,1};
	// 	while(*q){
	// 		ll t=*p/ *q;
	// 		rep(i,3) swap(p[i]-=t*q[i],q[i]);
	// 	}
	// 	if(p[0]<0) rep(i,3) p[i]=-p[i];
	// 	x=p[1],y=p[2];
	// 	return p[0];
	// }
	// ModInt inv() const {
	// 	ll x,y;
	// 	extgcd(v,mod,x,y);
	// 	return make(normS(x+mod));
	// }

	bool operator==(const ModInt& b) const { return v==b.v;}
	bool operator!=(const ModInt& b) const { return v!=b.v;}
	bool operator<(const ModInt& b) const { return v<b.v;}
	friend istream& operator>>(istream &o,ModInt& x){
		ll tmp;
		o>>tmp;
		x=ModInt(tmp);
		return o;
	}
	friend ostream& operator<<(ostream &o,const ModInt& x){ return o<<x.v;}
};
using mint = ModInt<998244353>;
//using mint = ModInt<1000000007>;
int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);		//DON'T USE scanf/printf/puts !!
	cout << fixed << setprecision(20);

	int N; cin >> N;
	V<mint> mu(N+1); mu[1] = 1;
	rep1(i,N){
		for(int j=i+i;j<=N;j+=i) mu[j] -= mu[i];
	}
	V<mint> f(N+1);
	rep1(i,N) f[i] = mu[i] * mint(2).pow(N/i);
	V<mint> F(N+1);
	rep1(i,N){
		for(int j=i;j<=N;j+=i) F[j] += f[i];
	}
	V<mint> G(N+1);
	rep1(i,N) G[i] = F[i] * F[i];
	rep1(i,N){
		for(int j=i+i;j<=N;j+=i) G[j] -= G[i];
	}
	mint allsum = accumulate(all(f),mint(0)).pow(2);
	mint ans = 0;
	mint oh = mint(3)/4;
	rep1(i,N) ans += G[i] * oh.pow(N/i);
	mint big = allsum - accumulate(all(G),mint(0));
	ans += big;
	{
		mint MU = accumulate(all(mu),mint(0));
		rep1(i,N) ans -= f[i] * MU * 2;
		ans += MU*MU;
	}
	cout << ans << endl;
// 	{
// 		mint god = 0;
// 		show(f);
// 		show(mu);
// 		rep1(i,N) rep1(j,N){
// 			int l = i*j/__gcd(i,j);
// 			int two = N/i+N/j-N/l*2;
// 			int three = N/l;
// 			mint waf = mint(2).pow(two) * mint(3).pow(three) - mint(2).pow(N/i) - mint(2).pow(N/j) + 1;
// 			god += mu[i] * mu[j] * waf;
// //			shows(i,j,waf);
// 		}
// 		show(god);
// 	}
}