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 AssimilationIV implements Runnable {

    void solve() {
        mod = 998244353;
        int n = ri(), m = ri();
        int[][] arr = new int[m][n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[j][i] = ri();
            }
        }

        long[] fac = lArr(n + 1);
        fac[1] = fac[0] = 1;
        for (int i = 2; i <= n; i++) {
            fac[i] = mul(fac[i - 1], i);
        }
        // For point j to not be captured by any city i, the monument should be built on
        // Steps >= n + 1 - x(distance)
        long res = 0;
        for (int i = 0; i < m; i++) {
            long curr = 1;
            Arrays.sort(arr[i]);
            for (int j = 0; j < n; j++) {
                int size = arr[i][j] - j - 1;
                size = max(size, 0);
                curr = mul(curr, size);
            }
            res = add(res, fac[n] - curr);
        }
        println(mul(res, inv(fac[n])));
    }

    long add(long a, long b) {
        return (a + b + mod) % mod;
    }

    long sub(long a, long b) {
        return (a - b) % mod;
    }

    long inv(long a) {
        return biPower(a, mod - 2);
    }

    long biPower(long a, long b) {
        long res = 1;
        while (b > 0) {
            if ((b & 1) == 1) {
                res = mul(res, a);
            }
            b >>= 1;
            a = mul(a, a);
        }
        return res;
    }

    long mul(long a, long b) {
        return (a * b) % mod;
    }

    long nor(long a) {
        if (a < mod)
            a += mod;
        return a;
    }

    /************************************************************************************************************************************************/
    public static void main(String[] args) throws IOException {
        new Thread(null, new AssimilationIV(), "1").start();
    }

    static PrintWriter out = new PrintWriter(System.out);
    static Reader read = new Reader();
    static StringBuilder sbr = new StringBuilder();
    static int mod = (int) 1e9 + 7;
    static int dmax = Integer.MAX_VALUE;
    static long lmax = Long.MAX_VALUE;
    static int dmin = Integer.MIN_VALUE;
    static long lmin = Long.MIN_VALUE;
    static int[] dprimes = new int[]{1, 11, 101, 1087, 99991, 100001, 1000003, 15485863, 999999937};

    @Override
    public void run() {
        solve();
        out.close();
    }

    static class Reader {
        private byte[] buf = new byte[1024];
        private int index;
        private InputStream in;
        private int total;

        public Reader() {
            in = System.in;
        }

        public int scan() throws IOException {
            if (total < 0)
                throw new InputMismatchException();
            if (index >= total) {
                index = 0;
                total = in.read(buf);
                if (total <= 0)
                    return -1;
            }
            return buf[index++];
        }

        public int intNext() throws IOException {
            int integer = 0;
            int n = scan();
            while (isWhiteSpace(n))
                n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                } else
                    throw new InputMismatchException();
            }
            return neg * integer;
        }

        public double doubleNext() throws IOException {
            double doub = 0;
            int n = scan();
            while (isWhiteSpace(n))
                n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n) && n != '.') {
                if (n >= '0' && n <= '9') {
                    doub *= 10;
                    doub += n - '0';
                    n = scan();
                } else
                    throw new InputMismatchException();
            }
            if (n == '.') {
                n = scan();
                double temp = 1;
                while (!isWhiteSpace(n)) {
                    if (n >= '0' && n <= '9') {
                        temp /= 10;
                        doub += (n - '0') * temp;
                        n = scan();
                    } else
                        throw new InputMismatchException();
                }
            }
            return doub * neg;
        }

        public String read() throws IOException {
            StringBuilder sb = new StringBuilder();
            int n = scan();
            while (isWhiteSpace(n))
                n = scan();
            while (!isWhiteSpace(n)) {
                sb.append((char) n);
                n = scan();
            }
            return sb.toString();
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1)
                return true;
            return false;
        }
    }

    // Gives strict lowerBound that previous number would be smaller than the target
    int lowerBound(int[] arr, int val) {
        int l = 0, r = arr.length - 1;
        while (l < r) {
            int mid = (r + l) >> 1;
            if (arr[mid] >= val) {
                r = mid;
            } else
                l = mid + 1;
        }
        return l;
    }

    // Gives strict upperBound that next number would be greater than the target
    int upperBound(int[] arr, int val) {
        int l = 0, r = arr.length - 1;
        while (l < r) {
            int mid = (r + l + 1) >> 1;
            if (arr[mid] <= val) {
                l = mid;
            } else
                r = mid - 1;
        }
        return l;
    }

    static void print(Object object) {
        out.print(object);
    }

    static void println(Object object) {
        out.println(object);
    }

    static int[] iArr(int len) {
        return new int[len];
    }

    static long[] lArr(int len) {
        return new long[len];
    }

    static long min(long a, long b) {
        return Math.min(a, b);
    }

    static int min(int a, int b) {
        return Math.min(a, b);
    }

    static long max(Long a, Long b) {
        return Math.max(a, b);
    }

    static int max(int a, int b) {
        return Math.max(a, b);
    }

    static int ri() {
        try {
            return read.intNext();
        } catch (IOException e) {
            e.printStackTrace();
        }
        System.exit(2);
        return -1;
    }

    static long rl() {
        try {
            return Long.parseLong(read.read());
        } catch (IOException e) {
            e.printStackTrace();
        }
        System.exit(2);
        return -1;
    }

    static String rs() {
        try {
            return read.read();
        } catch (IOException e) {
            e.printStackTrace();
        }
        System.exit(2);
        return "";
    }

    static char rc() {
        return rs().charAt(0);
    }

    static double rd() {
        try {
            return read.doubleNext();
        } catch (IOException e) {
            e.printStackTrace();
        }
        System.exit(2);
        return -1;
    }
}
