#include <bits/stdc++.h>
using namespace std;

const int maxn = 310, P = 998244353;
int n, m, a[maxn][maxn], b[maxn][maxn];

int qp(int x, int y) {
    int z = 1;
    for (; y; y >>= 1, x = 1LL * x * x % P) {
        if (y & 1)
            z = 1LL * z * x % P;
    }
    return z;
}

int main() {
    scanf("%d %d", &n, &m);
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= m; j++) {
            scanf("%d", &a[i][j]);
        }
    }
    for (int i = 1; i <= n; i++) {
        for (int j = m; j; j--)
            if (a[i][j]) {
                if (b[j][j]) {
                    for (int k = 1; k <= m; k++) {
                        a[i][k] ^= b[j][k];
                    }
                } else {
                    for (int k = 1; k <= m; k++) {
                        b[j][k] = a[i][k];
                    }
                    break;
                }
            }
    }
    int cnt = 0;
    for (int i = 1; i <= m; i++) {
        if (b[i][i])
            cnt++;
    }
    int ans = qp(2, n + m) - qp(2, n + m - cnt) + P;
    printf("%lld\n", 1LL * ans * qp(2, P - 2) % P);
    return 0;
}
### Prompt

Your task is to create 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 <bits/stdc++.h>
using namespace std;

const int maxn = 310, P = 998244353;
int n, m, a[maxn][maxn], b[maxn][maxn];

int qp(int x, int y) {
    int z = 1;
    for (; y; y >>= 1, x = 1LL * x * x % P) {
        if (y & 1)
            z = 1LL * z * x % P;
    }
    return z;
}

int main() {
    scanf("%d %d", &n, &m);
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= m; j++) {
            scanf("%d", &a[i][j]);
        }
    }
    for (int i = 1; i <= n; i++) {
        for (int j = m; j; j--)
            if (a[i][j]) {
                if (b[j][j]) {
                    for (int k = 1; k <= m; k++) {
                        a[i][k] ^= b[j][k];
                    }
                } else {
                    for (int k = 1; k <= m; k++) {
                        b[j][k] = a[i][k];
                    }
                    break;
                }
            }
    }
    int cnt = 0;
    for (int i = 1; i <= m; i++) {
        if (b[i][i])
            cnt++;
    }
    int ans = qp(2, n + m) - qp(2, n + m - cnt) + P;
    printf("%lld\n", 1LL * ans * qp(2, P - 2) % P);
    return 0;
}
```