#include <bits/stdc++.h>

using namespace std;

const int MOD = 998244353;
const int MaxN = 303;

int a[MaxN][MaxN];
int n, m;

int main()
{
    ios_base :: sync_with_stdio(false);
    cin.tie(NULL);
//    freopen("input.txt", "r", stdin);

    cin >> n >> m;
    for(int i = 1; i <= n; ++i)
        for(int j = 1; j <= m; ++j)
            cin >> a[i][j];

    int r = 0;

    for(int i = 1; i <= m; ++i)
    {
        int y = 0;
        for(int j = 1; y == 0 && j <= n; ++j)
            if(a[j][i] == 1)
                y = j;

        if(!y)
            continue;

        ++r;

        for(int j = 1; j <= n; ++j)
            if(a[j][i] == 1 && j != y)
                for(int k = i; k <= m; ++k)
                    a[j][k] ^= a[y][k];

        for(int k = i; k <= m; ++k)
            a[y][k] = 0;
    }

    int ans = 1;

    for(int i = 1; i <= n + m - 1; ++i)
        ans = (ans + ans) % MOD;

    int s = 1;
    for(int i = 1; i <= n + m - 1 - r; ++i)
        s = (s + s) % MOD;

    ans -= s;

    if(ans < 0)
        ans += MOD;
    cout << ans << '\n';

    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 <bits/stdc++.h>

using namespace std;

const int MOD = 998244353;
const int MaxN = 303;

int a[MaxN][MaxN];
int n, m;

int main()
{
    ios_base :: sync_with_stdio(false);
    cin.tie(NULL);
//    freopen("input.txt", "r", stdin);

    cin >> n >> m;
    for(int i = 1; i <= n; ++i)
        for(int j = 1; j <= m; ++j)
            cin >> a[i][j];

    int r = 0;

    for(int i = 1; i <= m; ++i)
    {
        int y = 0;
        for(int j = 1; y == 0 && j <= n; ++j)
            if(a[j][i] == 1)
                y = j;

        if(!y)
            continue;

        ++r;

        for(int j = 1; j <= n; ++j)
            if(a[j][i] == 1 && j != y)
                for(int k = i; k <= m; ++k)
                    a[j][k] ^= a[y][k];

        for(int k = i; k <= m; ++k)
            a[y][k] = 0;
    }

    int ans = 1;

    for(int i = 1; i <= n + m - 1; ++i)
        ans = (ans + ans) % MOD;

    int s = 1;
    for(int i = 1; i <= n + m - 1 - r; ++i)
        s = (s + s) % MOD;

    ans -= s;

    if(ans < 0)
        ans += MOD;
    cout << ans << '\n';

    return 0;
}

```