Monocarp is playing a game "Assimilation IV". In this game he manages a great empire: builds cities and conquers new lands.

Monocarp's empire has n cities. In order to conquer new lands he plans to build one Monument in each city. The game is turn-based and, since Monocarp is still amateur, he builds exactly one Monument per turn.

Monocarp has m points on the map he'd like to control using the constructed Monuments. For each point he knows the distance between it and each city. Monuments work in the following way: when built in some city, a Monument controls all points at distance at most 1 to this city. Next turn, the Monument controls all points at distance at most 2, the turn after — at distance at most 3, and so on. Monocarp will build n Monuments in n turns and his empire will conquer all points that are controlled by at least one Monument.

Monocarp can't figure out any strategy, so during each turn he will choose a city for a Monument randomly among all remaining cities (cities without Monuments). Monocarp wants to know how many points (among m of them) he will conquer at the end of turn number n. Help him to calculate the expected number of conquered points!

Input

The first line contains two integers n and m (1 ≤ n ≤ 20; 1 ≤ m ≤ 5 ⋅ 10^4) — the number of cities and the number of points.

Next n lines contains m integers each: the j-th integer of the i-th line d_{i, j} (1 ≤ d_{i, j} ≤ n + 1) is the distance between the i-th city and the j-th point.

Output

It can be shown that the expected number of points Monocarp conquers at the end of the n-th turn can be represented as an irreducible fraction x/y. Print this fraction modulo 998 244 353, i. e. value x ⋅ y^{-1} mod 998244353 where y^{-1} is such number that y ⋅ y^{-1} mod 998244353 = 1.

Example

Input


3 5
1 4 4 3 4
1 4 1 4 2
1 4 4 4 3


Output


166374062

Note

Let's look at all possible orders of cities Monuments will be build in: 

  * [1, 2, 3]: 
    * the first city controls all points at distance at most 3, in other words, points 1 and 4; 
    * the second city controls all points at distance at most 2, or points 1, 3 and 5; 
    * the third city controls all points at distance at most 1, or point 1. 
In total, 4 points are controlled. 
  * [1, 3, 2]: the first city controls points 1 and 4; the second city — points 1 and 3; the third city — point 1. In total, 3 points. 
  * [2, 1, 3]: the first city controls point 1; the second city — points 1, 3 and 5; the third city — point 1. In total, 3 points. 
  * [2, 3, 1]: the first city controls point 1; the second city — points 1, 3 and 5; the third city — point 1. In total, 3 points. 
  * [3, 1, 2]: the first city controls point 1; the second city — points 1 and 3; the third city — points 1 and 5. In total, 3 points. 
  * [3, 2, 1]: the first city controls point 1; the second city — points 1, 3 and 5; the third city — points 1 and 5. In total, 3 points. 

The expected number of controlled points is (4 + 3 + 3 + 3 + 3 + 3)/(6) = 19/6 or 19 ⋅ 6^{-1} ≡ 19 ⋅ 166374059 ≡ 166374062 \pmod{998244353}
#include <iostream>
#include <iomanip>
#include <fstream>
#include <vector>
#include <array>
#include <algorithm>
#include <utility>
#include <map>
#include <queue>
#include <set>
#include <cmath>
#include <cstdio>
#include <cstring>

#define ll long long
#define ld long double
#define eps 1e-8
#define MOD 998244353

#define INF 0x3f3f3f3f
#define INFLL 0x3f3f3f3f3f3f3f3f

// change if necessary
#define MAXN 1000000

using namespace std;

struct mi {
    int v;
    mi() : mi(0) {}
    mi(int v) : v(v) {}

    mi &operator+=(const mi &m2) {
        v += m2.v;
        if (v >= MOD) v -= MOD;
        return *this;
    }

    mi operator+(const mi &m2) const {
        mi m = *this;
        return m += m2;
    }

    mi &operator-=(const mi &m2) {
        v -= m2.v;
        if (v < 0) v += MOD;
        return *this;
    }

    mi operator-(const mi &m2) const {
        mi m = *this;
        return m -= m2;
    }

    mi &operator*=(const mi &m2) {
        v = (ll) v * m2.v % MOD;
        return *this;
    }

    mi operator*(const mi &m2) const {
        mi m = *this;
        return m *= m2;
    }

    mi pow(ll e) const {
        mi res = 1;
        mi n = *this;
        while (e) {
            if (e & 1) res *= n;
            n *= n;
            e >>= 1;
        }
        return res;
    }

    mi inv() const {
        return pow(MOD - 2);
    }
};

mi no_match(int n, const vector<int> &loc) {
    mi res = 1;
    for (int i = 0; i < n; i++) {
        int opt = loc[i] - i - 1;
        if (opt <= 0) {
            return 0;
        }
        res *= opt;
    }
    return res;
}

int main() {
    cin.tie(0)->sync_with_stdio(0);

    int n, m; cin >> n >> m;
    vector<vector<int>> dist(m);

    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            int x; cin >> x;
            dist[j].push_back(x);
        }
    }

    mi invf = 1;
    for (int i = 1; i <= n; i++) {
        invf *= i;
    }
    invf = invf.inv();

    mi ans = 0;
    for (int i = 0; i < m; i++) {
        sort(dist[i].begin(), dist[i].end());
        ans += (mi(1) - no_match(n, dist[i]) * invf); 
    }

    cout << ans.v << '\n';

    return 0;
}
