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}
# O(n^2*m + mlog(mod))
import sys
input = sys.stdin.buffer.readline

mod = 998244353

ans = 0

n,m = map(int,input().split())

fact = 1
for i in range(2,n+1):
    fact = fact * i  % mod
inv_fact = pow(fact,mod-2,mod)

dist = [list(map(int,input().split())) for i in range(n)]

# find expected value of each point (LOE)
for point in range(m):
    # if built at or after this time the point will not be conquered by that city
    time = [n+1 - dist[city][point] + 1 for city in range(n)]

    add = [0] * (n + 2)
    for i in time:
        add[i] += 1

    # of ways to place monuments so that they will not conquer the city
    dp = [[0]*(n+1) for i in range(n+2)] # dp[time][to place (at curr time)]

    dp[0][0] = 1

    for t in range(n+1):
        for to_place in range(n+1):
            if dp[t][to_place]:
                # don't place monument
                dp[t+1][to_place+add[t+1]] = (dp[t+1][to_place+add[t+1]] + dp[t][to_place]) % mod
                # place monument
                if to_place:
                    dp[t+1][to_place-1+add[t+1]] = (dp[t+1][to_place-1+add[t+1]] + to_place*dp[t][to_place]) % mod

    ans = (ans + (fact - dp[n+1][0])*inv_fact) % mod

print(ans)