#include <bits/stdc++.h>
using namespace std;
 
#define ll long long
#define all(aaa) aaa.begin(), aaa.end()

const int N = 305, MOD = 998244353;
bitset<N> b[N];

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int n, m;
    cin >> n >> m;

    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            int x;
            cin >> x;
            b[i][j] = x;
        }
    }

    ll bad = 1;

    for (int i = 0, j = 0; i < m; i++) {
        int sel = -1;
        for (int k = j; k < n; k++) {
            if (b[k][i] == 1) {
                sel = k;
                break;
            }
        }
        if (sel == -1) {
            bad = bad * 2 % MOD;
        }
        else {
            swap(b[sel], b[j]);
            for (int k = 0; k < n; k++) {
                if (k != j && b[k][i] == 1) {
                    b[k] ^= b[j];
                }
            }
            j++;
        }
    }

    ll ans = 1;
    for (int i = 0; i < m; i++) {
        ans = ans * 2 % MOD;
    }

    ans = (ans - bad + MOD) % MOD;

    for (int i = 0; i < n - 1; i++) {
        ans = ans * 2 % MOD;
    }

    cout << ans << "\n";

    return 0;
}
### Prompt

Please create a solution in CPP 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;
 
#define ll long long
#define all(aaa) aaa.begin(), aaa.end()

const int N = 305, MOD = 998244353;
bitset<N> b[N];

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int n, m;
    cin >> n >> m;

    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            int x;
            cin >> x;
            b[i][j] = x;
        }
    }

    ll bad = 1;

    for (int i = 0, j = 0; i < m; i++) {
        int sel = -1;
        for (int k = j; k < n; k++) {
            if (b[k][i] == 1) {
                sel = k;
                break;
            }
        }
        if (sel == -1) {
            bad = bad * 2 % MOD;
        }
        else {
            swap(b[sel], b[j]);
            for (int k = 0; k < n; k++) {
                if (k != j && b[k][i] == 1) {
                    b[k] ^= b[j];
                }
            }
            j++;
        }
    }

    ll ans = 1;
    for (int i = 0; i < m; i++) {
        ans = ans * 2 % MOD;
    }

    ans = (ans - bad + MOD) % MOD;

    for (int i = 0; i < n - 1; i++) {
        ans = ans * 2 % MOD;
    }

    cout << ans << "\n";

    return 0;
}
```