Problem: Kavi has 2n points lying on the OX axis, i-th of which is located at x = i.

Kavi considers all ways to split these 2n points into n pairs. Among those, he is interested in good pairings, which are defined as follows:

Consider n segments with ends at the points in correspondent pairs. The pairing is called good, if for every 2 different segments A and B among those, at least one of the following holds:

  * One of the segments A and B lies completely inside the other. 
  * A and B have the same length. 



Consider the following example:

<image>

A is a good pairing since the red segment lies completely inside the blue segment.

B is a good pairing since the red and the blue segment have the same length.

C is not a good pairing since none of the red or blue segments lies inside the other, neither do they have the same size.

Kavi is interested in the number of good pairings, so he wants you to find it for him. As the result can be large, find this number modulo 998244353.

Two pairings are called different, if some two points are in one pair in some pairing and in different pairs in another.

Input

The single line of the input contains a single integer n (1≤ n ≤ 10^6).

Output

Print the number of good pairings modulo 998244353.

Examples

Input


1


Output


1

Input


2


Output


3

Input


3


Output


6

Input


100


Output


688750769

Note

The good pairings for the second example are: 

<image>

In the third example, the good pairings are: 

<image>

Solution (in CPP):

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

using ll = long long;
using ld = long double;
using db = double;
using str = string; // yay python!

using pi = pair<int,int>;
using pl = pair<ll,ll>;
using pd = pair<db,db>;

using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>;
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;

#define tcT template<class T
#define tcTU tcT, class U
tcT> using V = vector<T>;
tcT, size_t SZ> using AR = array<T,SZ>;
tcT> using PR = pair<T,T>;

#define mp make_pair
#define fi first
#define se second

#define sz(x) int((x).size())
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend()
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pb push_back
#define eb emplace_back
#define pf push_front

#define lb lower_bound
#define ub upper_bound
tcT> int lwb(V<T>& a, const T& b) { return int(lb(all(a),b)-bg(a)); }

// loops
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)

const int MOD = 998244353;
const int MX = 2e5+5;
const ll INF = 1e18; 
const int dx[4] = {1,0,-1,0}, dy[4] = {0,1,0,-1};
template<class T> using pqg = priority_queue<T,vector<T>,greater<T>>;

tcT> bool ckmin(T& a, const T& b) {
	return b < a ? a = b, 1 : 0; }
tcT> bool ckmax(T& a, const T& b) {
	return a < b ? a = b, 1 : 0; }

#define tcTUU tcT, class ...U

// TO_STRING
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
str ts(bool b) {
	#ifdef LOCAL
		return b ? "true" : "false";
	#else
		return ts((int)b);
	#endif
}
tcTU> str ts(pair<T,U> p);
tcT> str ts(T v) {
	#ifdef LOCAL
		bool fst = 1; str res = "{";
		for (const auto& x: v) {
			if (!fst) res += ", ";
			fst = 0; res += ts(x);
		}
		res += "}"; return res;
	#else
		bool fst = 1; str res = "";
		for (const auto& x: v) {
			if (!fst) res += " ";
			fst = 0; res += ts(x);
		}
		return res;

	#endif
}
tcTU> str ts(pair<T,U> p) {
	#ifdef LOCAL
		return "("+ts(p.fi)+", "+ts(p.se)+")";
	#else
		return ts(p.fi)+" "+ts(p.se);
	#endif
}

tcT> void pr(T x) { cout << ts(x); }
tcTUU> void pr(const T& t, const U&... u) {
	pr(t); pr(u...); }
void ps() { pr("\n"); } 
tcTUU> void ps(const T& t, const U&... u) {
	pr(t); if (sizeof...(u)) pr(" "); ps(u...); }

// DEBUG
void DBG() { cerr << "]" << endl; }
tcTUU> void DBG(const T& t, const U&... u) {
	cerr << ts(t); if (sizeof...(u)) cerr << ", ";
	DBG(u...); }
#ifdef LOCAL
	#define dbg(...) cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
	#define chk(...) if (!(__VA_ARGS__)) cerr << "Line(" << __LINE__ << ") -> function(" \
		 << __FUNCTION__  << ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n", exit(0);
#else
	#define dbg(...) 0
	#define chk(...) 0
#endif

void setPrec() { cout << fixed << setprecision(15); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
void setIn(str s) { freopen(s.c_str(),"r",stdin); }
void setOut(str s) { freopen(s.c_str(),"w",stdout); }
void setIO(str s = "") {
	unsyncIO(); setPrec();
	if (sz(s)) setIn(s+".in"), setOut(s+".out");
}

const int nax = 1e6+10;
ll dp[nax];
int main() {
	setIO();

	ll n, s; cin >> n;
	fill(dp, dp+nax, 0);

	for(int i = 1; i <= n; i++) {
		for(int j = 2*i; j <= n; j += i) {
			dp[j]++;
		}
	}

	dp[0] = s = 1;
	for(int i = 1; i <= n; i++) {
		dp[i] = (dp[i] + s) % MOD;
		s = (s+dp[i]) % MOD;
	}
	cout << dp[n] << endl;
}