#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
using namespace std;
const int Mod=998244353;
int n,m;
#define Maxn 305
int num[Maxn][Maxn];
bool vis[Maxn];
int val[Maxn][Maxn];
inline int Fast_Pow(int a,int b){
	int ans=1;
	while(b){
		if(b&1)ans=1ll*ans*a%Mod;
		a=1ll*a*a%Mod;
		b>>=1;
	}
	return ans;
}

inline void rd(int &x){
	x=0;char ch=getchar();
	while(ch<'0'||ch>'9')ch=getchar();
	while(ch>='0'&&ch<='9'){
		x=x*10+ch-'0';
		ch=getchar();
	}
}

int main(){
	rd(n);rd(m);
	for(register int i=1;i<=n;++i)
	    for(register int j=1;j<=m;++j)rd(num[i][j]);
	int res=Fast_Pow(2,n);
	int T=0;
	for(register int i=1;i<=n;++i)
	    for(register int j=m;j>=1;--j)
	        if(num[i][j]){
				if(!vis[j]){
					for(register int k=1;k<=m;++k)val[j][k]=num[i][k];
					vis[j]=true;
					T++;
					break;
				}else{
					for(register int k=1;k<=m;++k)num[i][k]^=val[j][k];
				}
	        }
	res=(res-Fast_Pow(2,n-T)+Mod)%Mod;
	printf("%d\n",1ll*res*Fast_Pow(2,m-1)%Mod);
	return 0;
}
### Prompt

Create a solution in CPP for 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<cstring>
#include<cstdio>
#include<algorithm>
using namespace std;
const int Mod=998244353;
int n,m;
#define Maxn 305
int num[Maxn][Maxn];
bool vis[Maxn];
int val[Maxn][Maxn];
inline int Fast_Pow(int a,int b){
	int ans=1;
	while(b){
		if(b&1)ans=1ll*ans*a%Mod;
		a=1ll*a*a%Mod;
		b>>=1;
	}
	return ans;
}

inline void rd(int &x){
	x=0;char ch=getchar();
	while(ch<'0'||ch>'9')ch=getchar();
	while(ch>='0'&&ch<='9'){
		x=x*10+ch-'0';
		ch=getchar();
	}
}

int main(){
	rd(n);rd(m);
	for(register int i=1;i<=n;++i)
	    for(register int j=1;j<=m;++j)rd(num[i][j]);
	int res=Fast_Pow(2,n);
	int T=0;
	for(register int i=1;i<=n;++i)
	    for(register int j=m;j>=1;--j)
	        if(num[i][j]){
				if(!vis[j]){
					for(register int k=1;k<=m;++k)val[j][k]=num[i][k];
					vis[j]=true;
					T++;
					break;
				}else{
					for(register int k=1;k<=m;++k)num[i][k]^=val[j][k];
				}
	        }
	res=(res-Fast_Pow(2,n-T)+Mod)%Mod;
	printf("%d\n",1ll*res*Fast_Pow(2,m-1)%Mod);
	return 0;
}
```