#include <bits/stdc++.h>
    using namespace std;
    #define ll long long
    #define pb push_back
    #define mp make_pair
    const int N=305;
    const int mod=998244353;
    int a[N][N];
    int main()
    {
    	int n,m,i,j,k;
    	scanf("%i %i",&n,&m);
    	for(i=1;i<=n;i++) for(j=1;j<=m;j++) scanf("%i",&a[i][j]);
    	int r=0;
    	for(i=1;i<=m;i++)
    	{
    		bool ok=0;
    		for(j=r+1;j<=n;j++)
    		{
    			if(a[j][i])
    			{
    				for(k=i;k<=m;k++) swap(a[j][k],a[r+1][k]);
    				ok=1;
    				break;
    			}
    		}
    		if(!ok) continue;
    		r++;
    		for(j=r+1;j<=n;j++) if(a[j][i])
    		{
    			for(k=i;k<=m;k++) a[j][k]=(a[j][k]-a[r][k]+2)%2;
    		}
    	}
    	int ans=1,sol=1;
    	for(i=1;i<=n+m-1;i++) ans=ans*2%mod;
    	for(i=1;i<=n+m-r-1;i++) sol=sol*2%mod;
    	ans-=sol;
    	if(ans<0) ans+=mod;
    	printf("%i\n",ans);
    	return 0;
    }

### Prompt

Construct a Cpp code solution to the problem outlined:

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 pb push_back
    #define mp make_pair
    const int N=305;
    const int mod=998244353;
    int a[N][N];
    int main()
    {
    	int n,m,i,j,k;
    	scanf("%i %i",&n,&m);
    	for(i=1;i<=n;i++) for(j=1;j<=m;j++) scanf("%i",&a[i][j]);
    	int r=0;
    	for(i=1;i<=m;i++)
    	{
    		bool ok=0;
    		for(j=r+1;j<=n;j++)
    		{
    			if(a[j][i])
    			{
    				for(k=i;k<=m;k++) swap(a[j][k],a[r+1][k]);
    				ok=1;
    				break;
    			}
    		}
    		if(!ok) continue;
    		r++;
    		for(j=r+1;j<=n;j++) if(a[j][i])
    		{
    			for(k=i;k<=m;k++) a[j][k]=(a[j][k]-a[r][k]+2)%2;
    		}
    	}
    	int ans=1,sol=1;
    	for(i=1;i<=n+m-1;i++) ans=ans*2%mod;
    	for(i=1;i<=n+m-r-1;i++) sol=sol*2%mod;
    	ans-=sol;
    	if(ans<0) ans+=mod;
    	printf("%i\n",ans);
    	return 0;
    }

```