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 = [int(input().replace(" ",""),2) for i in range(n)]
mod = 998244353
cnt = 0
for j in range(m)[::-1]:
  for i in range(cnt,n):
    if a[i] & 1<<j:
      for k in range(n):
        if (i != k) and (a[k] & 1<<j):
          a[k] ^= a[i]
      a[i],a[cnt] = a[cnt],a[i]
      cnt += 1
if cnt == 0:
  print(0)
else:
  ans = pow(2,n+m-2*cnt,mod)*pow(2,cnt-1,mod)*(pow(2,cnt,mod)-1)%mod
  print(ans)