#include <iostream>
#include <bitset>
using namespace std;
const int MOD=998244353;
bitset<302> p[302],b[302],zero;
void insert(bitset<302> x) {
    for (int i = 301; i >= 0; i --) if (x[i]==1) {
        if ( p[i] != zero ) {
            x ^= p[i];
        } else {
            p[i] = x; 
            break;
        }
    }
} 
int n,m;
int main() {
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++){
        for(int j=1;j<=m;j++){
            int x; scanf("%d",&x);
            if(x) b[i][j]=1;
        }
        insert(b[i]);
    }

    int pivot=0;
    for(int i=0;i<302;i++){
        if(p[i] != zero) pivot ++;
    }
    int fre = n - pivot;
    int ans = 1, sub = 1;

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

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

    ans=1LL*ans*mul%MOD;
    cout<<ans<<endl;
}
### Prompt

In cpp, your task is to solve 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 <iostream>
#include <bitset>
using namespace std;
const int MOD=998244353;
bitset<302> p[302],b[302],zero;
void insert(bitset<302> x) {
    for (int i = 301; i >= 0; i --) if (x[i]==1) {
        if ( p[i] != zero ) {
            x ^= p[i];
        } else {
            p[i] = x; 
            break;
        }
    }
} 
int n,m;
int main() {
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++){
        for(int j=1;j<=m;j++){
            int x; scanf("%d",&x);
            if(x) b[i][j]=1;
        }
        insert(b[i]);
    }

    int pivot=0;
    for(int i=0;i<302;i++){
        if(p[i] != zero) pivot ++;
    }
    int fre = n - pivot;
    int ans = 1, sub = 1;

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

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

    ans=1LL*ans*mul%MOD;
    cout<<ans<<endl;
}
```