#include<bits/stdc++.h>

const int N = 310;
const int moder = 998244353;

std::bitset <N> set[N];
int power[N];

int main(){
    int n, m;
    scanf("%d%d", &n, &m);
    for (int i = 0; i < n; ++ i){
        for (int j = 0; j < m; ++ j){
            int x;
            scanf("%d", &x);
            set[i][j] = x;
        }
    }
    int now = 0;
    for (int i = 0; i < m; ++ i){
        for (int j = now; j < n; ++ j){
            if (set[j][i]){
                std::swap(set[now], set[j]);
                break;
            }
        }
        if (!set[now][i]){
            continue;
        }
        for (int j = now + 1; j < n; ++ j){
            if (set[j][i]){
                set[j] ^= set[now];
            }
        }
        ++ now;
    }
    power[0] = 1;
    for (int i = 1; i < N; ++ i){
        power[i] = 2 * power[i - 1] % moder;
    }
    int ans = (1ll * power[n] * (power[m - 1]) - 1ll * power[n - now] * power[m - 1]) % moder;
    ans += ans < 0 ? moder : 0;
    printf("%d\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<bits/stdc++.h>

const int N = 310;
const int moder = 998244353;

std::bitset <N> set[N];
int power[N];

int main(){
    int n, m;
    scanf("%d%d", &n, &m);
    for (int i = 0; i < n; ++ i){
        for (int j = 0; j < m; ++ j){
            int x;
            scanf("%d", &x);
            set[i][j] = x;
        }
    }
    int now = 0;
    for (int i = 0; i < m; ++ i){
        for (int j = now; j < n; ++ j){
            if (set[j][i]){
                std::swap(set[now], set[j]);
                break;
            }
        }
        if (!set[now][i]){
            continue;
        }
        for (int j = now + 1; j < n; ++ j){
            if (set[j][i]){
                set[j] ^= set[now];
            }
        }
        ++ now;
    }
    power[0] = 1;
    for (int i = 1; i < N; ++ i){
        power[i] = 2 * power[i - 1] % moder;
    }
    int ans = (1ll * power[n] * (power[m - 1]) - 1ll * power[n - now] * power[m - 1]) % moder;
    ans += ans < 0 ? moder : 0;
    printf("%d\n", ans);
    return 0;
}
```