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 <vector>
#include  <numeric>
#include<cstdlib>
#include <algorithm>    // std::random_shuffle
#define MODD 998244353
#define ll long long
using namespace std;

ll modpow(ll x, ll y) {
    ll xs = x;
    ll answer = 1;
    while(y) {
        if (y&1) {
            answer = (answer * xs) % MODD;
        }
        y >>= 1;
        xs = (xs * xs) % MODD ;
    }
    return answer;
}


ll D[22][55555];

char buf[58000000];

int pos;
ll readint() {
    while(buf[pos]<'0' || buf[pos]>'9')
        pos++;
    ll m=0;
    while(buf[pos]>='0' && buf[pos]<='9') {
        m=m*10+buf[pos]-'0';
        pos++;
    }
    return m;
}


int main() {
    fread(buf, 1, 51000100, stdin);
    pos=0;
    int n,m;
    n=readint();
    m=readint();
    for(int i=1;i<=n;i++) {
        for(int j=1;j<=m;j++) {
            D[i][j]=readint();
        }
    }

    ll fact = 1;
    for(ll i=1;i<=n;i++) {
        fact = (fact*i)%MODD;
    }

    ll factinv = modpow(fact, MODD-2);

    ll counts[22];
    ll ans = 0;
    for(int j=1;j<=m;j++) {
        for(int step=1;step<=n;step++) {
            // number of cities with distance >= step+1
            counts[step]=0;
            for(int i=1;i<=n;i++) {
                counts[step]+=(D[i][j]>=step+1);
            }
        }
        counts[n+1]=0;
        ll prod = 1;
        for(int step=n;step>=1;step--) {
            prod = (prod * (counts[step]-(n-step)))%MODD;
        }
        prod = (prod * factinv)%MODD;

        ll prob_selected = (1-prod+MODD)%MODD;
        ans += prob_selected;
        ans %= MODD;
    }

    ans = (ans + MODD)%MODD;

    cout << ans << endl;
}