#include<bits/stdc++.h>
#define rep(i,a,b) for(int i=a;i<=b;++i)
#define repd(i,a,b) for(int i=a;i>=b;--i)
#define rvc(i,S) for(int i=0;i<(int)S.size();++i)
#define fore(i,x) for(int i = head[x] ; i ; i = e[i].next)
#define mp make_pair
#define pb push_back
#define int long long
#define PII pair<int,int>
#define maxn 1000005
#define ll long long 
#define fi first
#define int ll
#define se second
#define debug(...) fprintf(stderr,__VA_ARGS__)
using namespace std; 
int n,m;
const int mo=998244353;
int a[305][305];
void SWAP(int x,int y)
{ rep(i,1,m) swap(a[x][i],a[y][i]);}
void solve(int x,int y)
{rep(i,1,m) a[x][i]^=a[y][i];
}
signed main()
{ cin>>n>>m;
  rep(i,1,n)rep(j,1,m) cin>>a[i][j];
  int r=0;
  rep(i,1,m)
  {int k=0; 
   rep(j,r+1,n) if(a[j][i]){k=j;break;}
   if(k) {r++;}
   else continue;
   SWAP(r,k);
   rep(p,1,n)
   {if((p!=r)&&a[p][i])
     solve(p,r);
   }
  }
  int add=1;
  rep(i,1,n+m-1) add=(add*2)%mo;
  int del=1;
  rep(i,1,n+m-r-1) del=(del*2)%mo;
  cout<<(add-del+mo)%mo<<endl; 
	
	
	
return 0;	
}
### Prompt

Your task is to create 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>
#define rep(i,a,b) for(int i=a;i<=b;++i)
#define repd(i,a,b) for(int i=a;i>=b;--i)
#define rvc(i,S) for(int i=0;i<(int)S.size();++i)
#define fore(i,x) for(int i = head[x] ; i ; i = e[i].next)
#define mp make_pair
#define pb push_back
#define int long long
#define PII pair<int,int>
#define maxn 1000005
#define ll long long 
#define fi first
#define int ll
#define se second
#define debug(...) fprintf(stderr,__VA_ARGS__)
using namespace std; 
int n,m;
const int mo=998244353;
int a[305][305];
void SWAP(int x,int y)
{ rep(i,1,m) swap(a[x][i],a[y][i]);}
void solve(int x,int y)
{rep(i,1,m) a[x][i]^=a[y][i];
}
signed main()
{ cin>>n>>m;
  rep(i,1,n)rep(j,1,m) cin>>a[i][j];
  int r=0;
  rep(i,1,m)
  {int k=0; 
   rep(j,r+1,n) if(a[j][i]){k=j;break;}
   if(k) {r++;}
   else continue;
   SWAP(r,k);
   rep(p,1,n)
   {if((p!=r)&&a[p][i])
     solve(p,r);
   }
  }
  int add=1;
  rep(i,1,n+m-1) add=(add*2)%mo;
  int del=1;
  rep(i,1,n+m-r-1) del=(del*2)%mo;
  cout<<(add-del+mo)%mo<<endl; 
	
	
	
return 0;	
}
```