p03133 Yahoo Programming Contest 2019 - Odd Subrectangles
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
```python
def rankmod2(A):
    global N, M
    ret = 0
    i = 0
    j = 0
    while i < N and j < M:
        if A[i][j]:
            ret += 1
        else:
            for ii in range(i+1, N):
                if A[ii][j]:
                    A[i], A[ii] = A[ii], A[i]
                    ret += 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 ret
                        
P = 998244353
N, M = map(int, input().split())
A = [list(map(int, input().split())) for _ in range(N)]
r = rankmod2(A)
print((pow(2, N+M-1, P)-pow(2, N+M-r-1, P)) % P)
```