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 

template <int mod = 1000000007>
struct modint{
    int x;
    modint(long long y = 0) : x((y % mod + mod) % mod) { }
    friend modint operator ^ (modint a, int64_t b) {
        modint r = 1;
        for(; b; b >>= 1, a *= a) if(b & 1) r *= a;
        return r;
    }
    friend modint operator - (modint a) {return modint(0) - a;}
    friend modint operator ! (modint a) {return a ^ (mod - 2);}
    modint& operator /= (modint const& b) {return *this *= !b;}
    friend modint operator + (modint a, modint const& b) {return a += b;}
    friend modint operator - (modint a, modint const& b) {return a -= b;}
    friend modint operator * (modint a, modint const& b) {return a *= b;}
    friend modint operator / (modint a, modint const& b) {return a /= b;}
    friend bool operator != (const modint &a, const modint b) {return a.x != b.x;}
    friend bool operator == (const modint &a, const modint b) {return a.x == b.x;}
    modint& operator *= (modint const& b) {x = 1LL * x * b.x % mod; return *this;}
    friend ostream& operator << (ostream& os, modint const& a) {return os << a.x;}
    modint& operator += (modint const& b) {x += b.x; x = (x >= mod) ? x - mod : x;return *this;}
    modint& operator -= (modint const& b) {x = x >= b.x ? x - b.x : x - b.x + mod;return *this;}
};

using mint = modint <998244353>;

namespace C{
    vector <mint> F, I;
    void init(int n) {
        F = I = vector <mint> (n + 1, 1);
        for(int i = 1; i <= n; i++) F[i] = F[i - 1] * i; 
        I[n] = !F[n];
        for(int i = n; i >= 1; i--) I[i - 1] = I[i] * i;
    }
    mint nCr(int n, int r) {
        return n >= r ? F[n] * I[r] * I[n - r] : 0;
    }
}




int32_t main() {
    ios_base :: sync_with_stdio(0); cin.tie(0); cout.tie(0);
    int n, m; cin >> n >> m;

    vector <vector <int>> a(n, vector <int> (m));

    for(auto &v: a)
        for(auto &x: v)
            cin >> x;

    C::init(n + 10);

    mint ans = 0;

    for(int i = 0; i < m; i++) {
        vector <int> c(n + 10);

        for(int j = 0; j < n; j++) {
            c[n - a[j][i] + 2]++;
        }

        mint q = 1;

        for(int j = 1; j <= n; j++) {
            c[j] += c[j - 1];
            if(c[j] - (j - 1) <= 0) {
                q = 0;
            } else {
                q *= (c[j] - (j - 1));
            }
        }

        ans += C::F[n] - q;
    }


    cout << ans / C::F[n] << endl;
}