#include <cstdio>
#include <algorithm>
using namespace std;

const int MOD = 998244353;

bool p[302][302];

int _pow(int x){
  int v = 1, w = 2;

  while(x > 0){
    if(x & 1) v = 1LL * v * w % MOD;
    w = 1LL * w * w % MOD; x >>= 1;
  }

  return v;
}

int main(){
  int N, M; scanf("%d%d", &N, &M);

  for(int i = 1; i <= N; i++){
    for(int j = 1; j <= M; j++){
      int x; scanf("%d", &x); p[i][j] = x == 1;
    }
  }

  int f = 0;

  for(int i = 1; i <= M; i++){
    int z = 0;

    for(int j = f + 1; j <= N; j++){
      if(p[j][i]){ z = j; break; }
    }

    if(z == 0) continue;

    f++;
    for(int j = 1; j <= M; j++) swap(p[f][j], p[z][j]);

    for(int j = 1; j <= N; j++){
      if(j == f) continue;

      if(p[j][i]){
        for(int k = 1; k <= M; k++) p[j][k] ^= p[f][k];
      }
    }
  }

  int a = _pow(N), b = _pow(N - f), c = _pow(M - 1);
  int ans = 1LL * (a - b < 0 ? a - b + MOD : a - b) * c % MOD;

  printf("%d\n", ans);
  return 0;
}
### Prompt

Generate a Cpp solution to the following problem:

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

### Response

```cpp
#include <cstdio>
#include <algorithm>
using namespace std;

const int MOD = 998244353;

bool p[302][302];

int _pow(int x){
  int v = 1, w = 2;

  while(x > 0){
    if(x & 1) v = 1LL * v * w % MOD;
    w = 1LL * w * w % MOD; x >>= 1;
  }

  return v;
}

int main(){
  int N, M; scanf("%d%d", &N, &M);

  for(int i = 1; i <= N; i++){
    for(int j = 1; j <= M; j++){
      int x; scanf("%d", &x); p[i][j] = x == 1;
    }
  }

  int f = 0;

  for(int i = 1; i <= M; i++){
    int z = 0;

    for(int j = f + 1; j <= N; j++){
      if(p[j][i]){ z = j; break; }
    }

    if(z == 0) continue;

    f++;
    for(int j = 1; j <= M; j++) swap(p[f][j], p[z][j]);

    for(int j = 1; j <= N; j++){
      if(j == f) continue;

      if(p[j][i]){
        for(int k = 1; k <= M; k++) p[j][k] ^= p[f][k];
      }
    }
  }

  int a = _pow(N), b = _pow(N - f), c = _pow(M - 1);
  int ans = 1LL * (a - b < 0 ? a - b + MOD : a - b) * c % MOD;

  printf("%d\n", ans);
  return 0;
}
```