#include<bits/stdc++.h>
using namespace std;
const int mo=998244353,N=305;
int mi[N],n,m,i,j,k,a[N][N];
bitset<N>b[N],x;
int main(){
	for(i=*mi=1;i<N;++i)mi[i]=2ll*mi[i-1]%mo;
	scanf("%d%d",&n,&m);
	for(i=1;i<=n;++i){
		x.reset();
		for(j=0;j<m;++j)scanf("%d",a[i]+j),x.set(j,a[i][j]);
		for(j=0;j<m;++j)if(x[j]){
			if(b[j].any())x^=b[j];
				else{b[j]=x;break;}
		}
		if(j==m)++k;
	}
	i=(1ll*mi[m]*mi[k]+1ll*mi[m-1]*(mi[n]+mo-mi[k]))%mo;
	i=(1ll*mi[n]*mi[m]+mo-i)%mo;
	printf("%d\n",i);
	return 0;
}
### 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<bits/stdc++.h>
using namespace std;
const int mo=998244353,N=305;
int mi[N],n,m,i,j,k,a[N][N];
bitset<N>b[N],x;
int main(){
	for(i=*mi=1;i<N;++i)mi[i]=2ll*mi[i-1]%mo;
	scanf("%d%d",&n,&m);
	for(i=1;i<=n;++i){
		x.reset();
		for(j=0;j<m;++j)scanf("%d",a[i]+j),x.set(j,a[i][j]);
		for(j=0;j<m;++j)if(x[j]){
			if(b[j].any())x^=b[j];
				else{b[j]=x;break;}
		}
		if(j==m)++k;
	}
	i=(1ll*mi[m]*mi[k]+1ll*mi[m-1]*(mi[n]+mo-mi[k]))%mo;
	i=(1ll*mi[n]*mi[m]+mo-i)%mo;
	printf("%d\n",i);
	return 0;
}
```