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}
mod = 998244353
def gcd(a,b):
    if a == 0 or b == 0:
        return 1
    while b:
        a,b=b,a%b
    return a
def gcdExtended(a, b): 
    # Base Case 
    if a == 0 :  
        return b,0,1
             
    gcd,x1,y1 = gcdExtended(b%a, a) 
     
    # Update x and y using results of recursive 
    # call 
    x = y1 - (b//a) * x1 
    y = x1 
     
    return gcd,x,y
def simpl(a):
    gecd = gcd(a[0],a[1])
    return (a[0]//gecd,a[1]//gecd)
def mulmod(a,b):
    a = summod(a,0)
    b = summod(b,0)
    return ((a%mod)*(b%mod))%mod
    # return a*b
def summod(a,b):
    return ((a%mod)+(b%mod)+mod)%mod
    # return a+b
def addfrac(a,b):
    a = (summod(a[0],0),summod(a[1],0))
    b = (summod(b[0],0),summod(b[1],0))
    gecd = gcd(a[1],b[1])
    lcm = a[1]//gecd*b[1]
    x = mulmod(a[0],b[1]//gecd)
    y = mulmod(b[0],a[1]//gecd)
    return simpl((summod(x,y),lcm))
    # return (a[0]*b[1]+b[0]*a[1],a[1]*b[1])
def mulfrac(a,b):
    return simpl((mulmod(a[0],b[0]),mulmod(a[1],b[1])))
    # return (a[0]*b[0],a[1]*b[1])

n,m = map(int,input().split())
dists = [[0 for j in range(n)] for i in range(m)]
out = (0,1)
for i in range(n):
    dist = list(map(int,input().split()))
    for j in range(m):
        dists[j][i] = dist[j]
for i in range(m):
    dists[i].sort()
out = 0
nfac = 1
for i in range(2,n+1):
    nfac = mulmod(nfac,i)
for i in range(m):
    cur = 1
    for j in range(n):
        cur = mulmod(cur,max(0,dists[i][j]-(j+1)))
    out = summod(out,cur)
# print(out)
# print(nfac)
out = mulfrac((-1,1),(out,nfac))
# print(out)
out = addfrac((m,1),out)
# print(out)
out = mulmod(out[0],(gcdExtended(out[1],mod)[1]+mod)%mod)
print(out)
