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
def rankmod2(A):
    n,m=len(A),len(A[0])
    rank=0
    i,j=0,0
    while i<n and j<m:
        if A[i][j]:
            rank+=1
        else:
            for ii in range(i+1,n):
                if A[ii][j]:
                    A[i],A[ii]=A[ii],A[i]
                    rank+=1
                    break
            else:
                j+=1
                continue
        for ii in range(i+1,n):
            if A[ii][j]:
                for jj in range(j,m):
                    A[ii][jj]=(A[ii][jj]+A[i][jj])% 2
        i+=1
        j+=1
    return rank

n,m=map(int,input().split())
mod=998244353
A=[list(map(int,input().split())) for _ in range(n)]
r=rankmod2(A)
ans=(pow(2,n+m-1,mod)-pow(2,n+m-r-1,mod))%mod
print(ans)