There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.

Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:

* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.

Constraints

* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}


Output

Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.

Examples

Input

2 2
0 1
1 0


Output

6


Input

2 3
0 0 0
0 1 0


Output

8
N,M=map(int,input().split())
a=[]
for i in range(N):
    a.append(list(map(int,input().split())))
mod=998244353

B=[]
for i in range(M):
    b=0
    for j in range(N):
        b+=a[j][i]*2**j
    B.append(b)

base=[]
for i in range(M):
    t=B[i]
    for b in base:
        t=min(t,t^b)
    if t!=0:
        base.append(t)

res=M-len(base)
ans=pow(2,N-1,mod)*(pow(2,M,mod)-pow(2,res,mod))
print(ans%mod)
