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}
import java.io.*;
import java.util.*;

public class E{
	
	static long mod = 998244353;
	
	static long mi(long a) {return pow(a,mod-2);}
	
	static long pow(long b, long e) {
		if (e==0)return 1;
		long r = pow(b,e/2);
		r = r*r%mod;
		if (e % 2 == 1) return r * b % mod;
		return r;
	}
	
	public static void main(String[] args) throws IOException {
		// br = new BufferedReader(new FileReader(".in"));
		// out = new PrintWriter(new FileWriter(".out"));
		read();
		int n = rI();
		int m = rI();
		Integer[][] a = new Integer[m][n];
		for (int i = 0; i < n; i++) {
			read();
			for (int j = 0; j < m; j++) {
				a[j][i] = rI();
			}
		}
		
		long fac = 1;
		for (int i =1; i <= n; i++) fac = fac * i %mod;
		
		long pts = 0;
		for (int i= 0 ; i < m; i++) {
			Arrays.sort(a[i]);
			// What are the chances that EVERY position in this permutation fails?
			// How man permutations strictly lexicographically (so no EQ) than this position?
			pts += fac;
			long cur = 1;
			for (int j =0 ; j < n; j++) {
				cur *= Long.max(0, a[i][j]-j-1);
				cur %= mod;
			}
			pts = (pts - cur + mod)%mod;
		}
		out.println(pts * mi(fac) % mod);
		out.close();
	}
	
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
	static StringTokenizer st;
	static void read() throws IOException{st = new StringTokenizer(br.readLine());}	
	static int rI() throws IOException{return Integer.parseInt(st.nextToken());}
	static long rL() throws IOException{return Long.parseLong(st.nextToken());}
	static double rD() throws IOException{return Double.parseDouble(st.nextToken());}
	
}
