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;

typedef long long ll;
typedef long double ld;

typedef vector<int> vi;
typedef vector<ll> vll;

typedef vector<vi> vvi;
typedef vector<vll> vvll;

typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

typedef vector<pii> vpii;
typedef vector<pll> vpll;

typedef vector<vpii> vvpii;
typedef vector<vpll> vvpll;

#define pb push_back
#define mp make_pair
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) (int)(x).size()
#define fi first
#define se second

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

namespace debug {
    void __print(int x) {cerr << x;}
    void __print(long long x) {cerr << x;}
    void __print(double x) {cerr << x;}
    void __print(long double x) {cerr << x;}
    void __print(char x) {cerr << '\'' << x << '\'';}
    void __print(const string &x) {cerr << '\"' << x << '\"';}
    void __print(bool x) {cerr << (x ? "true" : "false");}

    template<typename T, typename V>
    void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
    template<typename T>
    void __print(const T &x) {int f = 0; cerr << '{'; for(auto z : x) cerr << (f++ ? "," : ""), __print(z); cerr << "}";}
    void _print() {cerr << "]\n";}
    template <typename T, typename... V>
    void _print(T t, V... v) {__print(t); if(sizeof...(v)) cerr << ", "; _print(v...);}

#ifdef ljuba
#define dbg(x...) cerr << "LINE(" << __LINE__ << ") -> " << "[" << #x << "] = ["; _print(x)
#else
#define dbg(x...)
#endif
}

using namespace debug;

const char nl = '\n';

mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());

const int MOD = 998244353;

const int mxN = 1e6 + 12;
int dp[mxN];

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

    int pref = 1;
    for(int i = 1; i <= n; ++i) {
        dp[i] = (dp[i] + pref) % MOD;
        pref = (pref + dp[i]) % MOD;
    }

    cout << dp[n] << nl;
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    int testCases = 1;
    //cin >> testCases;
    while(testCases--)
        solve();

}