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 <bits/stdc++.h>

using namespace std;
#define int long long

const int mod = 998244353;
int n, m;
int bpow(int a, int b){
	int res = 1;
	while(b){
		if(b&1){
			res = (res *a)%mod;
		}
		a = (a*a)%mod;
		b >>=1 ;
	}
	return res;
}

void solve(){
	cin>>n>>m;
	vector<vector<int>> a(n, vector<int> (m));
	int f= 1;
	for(int i=0;i<n;i++){
		f *= (i+1);
		f %= mod;
		for(int j=0;j<m;j++){
			cin>>a[i][j];
		}
	}
	f= bpow(f, mod-2);
	int ans  =0;
	for(int j=0;j< m;j++){
		vector<int> cnt(n+1);
		for(int i=0;i<n;i++){
			cnt[n+1-a[i][j]]++;
		}
		int cur = 1;
		int take =0;
		for(int i=0;i<n;i++){
			cur *= max(0LL, cnt[i]+take-i);
			cur  %= mod;
			take += cnt[i];
		}
		ans += (1- ((cur*f)%mod) + mod)%mod;
		ans %= mod;
	}
	cout<<ans<<'\n';
}

int32_t main(){
	ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);

	int t;
	// cin>>t;
	t = 1;
	int _=1;
	while(t--){
		// cout<<"Case #"<<_++<<": ";
		solve();
	}
	return 0;
}