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;

#ifdef LOCAL
#define DEBUG(...) debug(#__VA_ARGS__, __VA_ARGS__)
#else
#define DEBUG(...) 6
#endif

template<typename T, typename S> ostream& operator << (ostream &os, const pair<T, S> &p) {return os << "(" << p.first << ", " << p.second << ")";}
template<typename C, typename T = decay<decltype(*begin(declval<C>()))>, typename enable_if<!is_same<C, string>::value>::type* = nullptr>
ostream& operator << (ostream &os, const C &c) {bool f = true; os << "["; for (const auto &x : c) {if (!f) os << ", "; f = false; os << x;} return os << "]";}
template<typename T> void debug(string s, T x) {cerr << s << " = " << x << "\n";}
template<typename T, typename... Args> void debug(string s, T x, Args... args) {for (int i=0, b=0; i<(int)s.size(); i++) if (s[i] == '(' || s[i] == '{') b++; else
if (s[i] == ')' || s[i] == '}') b--; else if (s[i] == ',' && b == 0) {cerr << s.substr(0, i) << " = " << x << " | "; debug(s.substr(s.find_first_not_of(' ', i + 1)), args...); break;}}

template<int MOD>
struct ModInt {
    long long v;
    ModInt(long long _v = 0) {v = (-MOD < _v && _v < MOD) ? _v : _v % MOD; if (v < 0) v += MOD;}
    ModInt& operator += (const ModInt &other) {v += other.v; if (v >= MOD) v -= MOD; return *this;}
    ModInt& operator -= (const ModInt &other) {v -= other.v; if (v < 0) v += MOD; return *this;}
    ModInt& operator *= (const ModInt &other) {v = v * other.v % MOD; return *this;}
    ModInt& operator /= (const ModInt &other) {return *this *= inverse(other);}
    bool operator == (const ModInt &other) const {return v == other.v;}
    bool operator != (const ModInt &other) const {return v != other.v;}
    friend ModInt operator + (ModInt a, const ModInt &b) {return a += b;}
    friend ModInt operator - (ModInt a, const ModInt &b) {return a -= b;}
    friend ModInt operator * (ModInt a, const ModInt &b) {return a *= b;}
    friend ModInt operator / (ModInt a, const ModInt &b) {return a /= b;}
    friend ModInt operator - (const ModInt &a) {return 0 - a;}
    friend ModInt power(ModInt a, long long b) {ModInt ret(1); while (b > 0) {if (b & 1) ret *= a; a *= a; b >>= 1;} return ret;}
    friend ModInt inverse(ModInt a) {return power(a, MOD - 2);}
    friend istream& operator >> (istream &is, ModInt &m) {is >> m.v; m.v = (-MOD < m.v && m.v < MOD) ? m.v : m.v % MOD; if (m.v < 0) m.v += MOD; return is;}
    friend ostream& operator << (ostream &os, const ModInt &m) {return os << m.v;}
};
typedef ModInt<998244353> M;

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

    int n, m;
    cin >> n >> m;
    vector<vector<int>> d(n, vector<int>(m));
    for (int i=0; i<n; i++)
        for (int j=0; j<m; j++)
            cin >> d[i][j];

    M fact = 1;
    for (int i=1; i<=n; i++)
        fact *= i;

    M ret = m * fact;
    for (int j=0; j<m; j++) {
        vector<int> cnt(n + 1);
        for (int i=0; i<n; i++)
            cnt[n - d[i][j] + 1]++;
        M cur = 1;
        int tot = 0;
        for (int i=0; i<n; i++) {
            tot += cnt[i];
            cur *= tot--;
        }
        ret -= cur;
    }
    cout << ret / fact << "\n";

    return 0;
}
