#include <cstdio>

using namespace std;

const int mod = 998244353;
int a[300][300];
long long b[301];
int f[300];

int main() {
    int n, m, c, i, j, k, l;
    long long ans = 0;
    
    scanf("%d %d", &n, &m);
    
    for (i = 0; i < n; i++) {
        for (j = 0; j < m; j++) {
            scanf("%d", &a[i][j]);
        }
    }
    
    b[0] = 1;
    for (i = 1; i <= 300; i++) b[i] = b[i - 1] * 2 % mod;
    
    c = m;
    
    for (i = 0; i < n; i++) {
        for (j = 0; j < m; j++) {
            if (f[j] == 1) continue;
            if (a[i][j] == 1) break;
        }
        
        if (j == m) continue;
        
        c--;
        f[j] = 1;
        
        for (k = j + 1; k < m; k++) {
            if (a[i][k] == 0) continue;
            
            for (l = i; l < n; l++) a[l][k] ^= a[l][j];
        }
        
        ans += b[c] * b[n - 1];
        ans %= mod;
    }
    
    printf("%lld\n", ans);
    
    return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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>

using namespace std;

const int mod = 998244353;
int a[300][300];
long long b[301];
int f[300];

int main() {
    int n, m, c, i, j, k, l;
    long long ans = 0;
    
    scanf("%d %d", &n, &m);
    
    for (i = 0; i < n; i++) {
        for (j = 0; j < m; j++) {
            scanf("%d", &a[i][j]);
        }
    }
    
    b[0] = 1;
    for (i = 1; i <= 300; i++) b[i] = b[i - 1] * 2 % mod;
    
    c = m;
    
    for (i = 0; i < n; i++) {
        for (j = 0; j < m; j++) {
            if (f[j] == 1) continue;
            if (a[i][j] == 1) break;
        }
        
        if (j == m) continue;
        
        c--;
        f[j] = 1;
        
        for (k = j + 1; k < m; k++) {
            if (a[i][k] == 0) continue;
            
            for (l = i; l < n; l++) a[l][k] ^= a[l][j];
        }
        
        ans += b[c] * b[n - 1];
        ans %= mod;
    }
    
    printf("%lld\n", ans);
    
    return 0;
}

```