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}
def get_one(ns,m):
    n=len(ns)
    ans=1
    for i in range(n):
        t=ns[i]-i
        if t<=0:
            return 0
        ans=ans*t%m
    return ans
def get_one_pre(ns:list):
    ans=[0]*len(ns)
    ns.sort()
    l=0
    for i in range(len(ns)):
        for j in range(l,len(ns)):
            if i+1<ns[j]:
                l = j
                ans[i] = len(ns) - l
                break
        else:
            l=j
            ans[i]=0
    return list(reversed(ans))
def pow(a,b,m):
    tb=[a]
    for i in range(35):
        tb.append(tb[-1]*tb[-1]%m)
    ans=1
    for i in range(35):
        if (b>>i)&1==1:
            ans=ans*tb[i]%m
    return ans
def inv(a,m):
    return pow(a,m-2,m)
def functoria(x,m):
    ans=1
    for i in range(1,x+1):
        ans=ans*i%m
    return ans

def gns():
    return list(map(int,input().split()))
def gn():
    return int(input())
n,m=gns()
md=998244353
ms=[[]for i in range(m)]
for i in range(n):
    ns=gns()
    for i in range(m):
        ms[i].append(ns[i])
sm=0
for i in range(m):
    x=get_one_pre(ms[i])
    y=get_one(x,md)
    sm=(sm+y)%md
f=functoria(n,md)
fv=inv(f,md)
ans=(f*m-sm+md)*fv%md
print(ans)