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.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.List;
 import java.util.*;
 public class realfast implements Runnable 
  {
    private static final int INF = (int) 1e9;
    long in= 998244353;
    long fac[]= new long[1000001];
    long inv[]=new long[1000001];
    public  void solve() throws IOException 
    {

        //int t = readInt();

        int n = readInt();
        int m = readInt();

        int arr[][]=new int[n+1][m+1];


        for(int i=1;i<=n;i++)
        {
            for(int j=1;j<=m;j++)
            {
                arr[i][j]= readInt();
            }
        }

        long pal = 1;
        for(int i=1;i<=n;i++)
        {
            pal= (pal*i)%in;
        }


      //  long gal =1;
        long ans=0;
        int count[]=new int[n+2];
        for(int j=1;j<=m;j++)
        {
             for(int i=0;i<=n+1;i++)
                count[i]=0;

             for(int i=1;i<=n;i++)
             {
                count[arr[i][j]]++;
             }

             long cal = 1;
             int sal=0;
             for(int i=n+1;i>=2;i--)
             {
                 sal =sal+count[i];
                 
                 
                 cal = (cal*sal)%in;
                 sal--;
                 if(sal<0)
                    sal=0;
             }

             ans = (ans%in+ (pal - cal+in)%in)%in;
        }

        ans = (ans*pow(pal,in-2,in))%in;

        out.println(ans);
        
      
             


         



        



    }
    
    public int value (int seg[], int left , int right ,int index, int l, int r)
    {
            
            if(left>right)
            {
              return -100000000;
            }
            if(right<l||left>r)
                return -100000000;
            if(left>=l&&right<=r)
                return seg[index];
            int mid = left+(right-left)/2;
            int val = value(seg,left,mid,2*index+1,l,r);
            int val2 = value(seg,mid+1,right,2*index+2,l,r);
            return Math.max(val,val2);

    }
   
    public int gcd(int a , int b )
    {
      if(a<b)
      {
        int t =a;
        a=b;
        b=t;
      }
      if(a%b==0)
        return b ;
      return gcd(b,a%b);
    }
    public long pow(long n , long p,long m)
    {
         if(p==0)
            return 1;
        long val = pow(n,p/2,m);;
        val= (val*val)%m;
        if(p%2==0)
            return val;
        else
            return (val*n)%m;
    }
    
    
    ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
    public static void main(String[] args) {
        new Thread(null, new realfast(), "", 128 * (1L << 20)).start();
    }
 
    private static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    private BufferedReader reader;
    private StringTokenizer tokenizer;
    private PrintWriter out;
 
    @Override
    public void run() {
        try {
            if (ONLINE_JUDGE || !new File("input.txt").exists()) {
                reader = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                reader = new BufferedReader(new FileReader("input.txt"));
                out = new PrintWriter("output.txt");
            }
            solve();
        } catch (IOException e) {
            throw new RuntimeException(e);
        } finally {
            try {
                reader.close();
            } catch (IOException e) {
                // nothing
            }
            out.close();
        }
    }
 
    private String readString() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
 
    @SuppressWarnings("unused")
    private int readInt() throws IOException {
        return Integer.parseInt(readString());
    }
 
    @SuppressWarnings("unused")
    private long readLong() throws IOException {
        return Long.parseLong(readString());
    }
 
    @SuppressWarnings("unused")
    private double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }
}
class edge implements Comparable<edge>{
    int u ;
    int v;
    
    edge(int u, int v)
    {
       this.u=u;
       this.v=v;
    }
    public int compareTo(edge e)
    {
        return this.v-e.v;
    }
}