#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<vector>
using namespace std;
#define ll long long
#define MOD 998244353
#define MAX 350
inline int read()
{
	int x=0;bool t=false;char ch=getchar();
	while((ch<'0'||ch>'9')&&ch!='-')ch=getchar();
	if(ch=='-')t=true,ch=getchar();
	while(ch<='9'&&ch>='0')x=x*10+ch-48,ch=getchar();
	return t?-x:x;
}
int fpow(int a,int b)
{
	int s=1;
	while(b){if(b&1)s=1ll*s*a%MOD;a=1ll*a*a%MOD;b>>=1;}
	return s;
}
int n,m,tot,a[MAX][MAX],s[MAX];
int p[MAX][MAX];bool vis[MAX];
void Insert(int x)
{
	for(int i=1;i<=m;++i)
		if(a[x][i])
		{
			if(vis[i])
			{
				for(int j=1;j<=m;++j)a[x][j]^=p[i][j];
				continue;
			}
			++tot;vis[i]=true;
			for(int j=1;j<=m;++j)p[i][j]=a[x][j];break;
		}
}
int main()
{
	n=read();m=read();
	for(int i=1;i<=n;++i)
		for(int j=1;j<=m;++j)
			a[i][j]=read();
	for(int i=1;i<=n;++i)Insert(i);
	int ans=1ll*(fpow(2,n)-fpow(2,n-tot)+MOD)*fpow(2,m-1)%MOD;
	printf("%d\n",ans);
	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<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<vector>
using namespace std;
#define ll long long
#define MOD 998244353
#define MAX 350
inline int read()
{
	int x=0;bool t=false;char ch=getchar();
	while((ch<'0'||ch>'9')&&ch!='-')ch=getchar();
	if(ch=='-')t=true,ch=getchar();
	while(ch<='9'&&ch>='0')x=x*10+ch-48,ch=getchar();
	return t?-x:x;
}
int fpow(int a,int b)
{
	int s=1;
	while(b){if(b&1)s=1ll*s*a%MOD;a=1ll*a*a%MOD;b>>=1;}
	return s;
}
int n,m,tot,a[MAX][MAX],s[MAX];
int p[MAX][MAX];bool vis[MAX];
void Insert(int x)
{
	for(int i=1;i<=m;++i)
		if(a[x][i])
		{
			if(vis[i])
			{
				for(int j=1;j<=m;++j)a[x][j]^=p[i][j];
				continue;
			}
			++tot;vis[i]=true;
			for(int j=1;j<=m;++j)p[i][j]=a[x][j];break;
		}
}
int main()
{
	n=read();m=read();
	for(int i=1;i<=n;++i)
		for(int j=1;j<=m;++j)
			a[i][j]=read();
	for(int i=1;i<=n;++i)Insert(i);
	int ans=1ll*(fpow(2,n)-fpow(2,n-tot)+MOD)*fpow(2,m-1)%MOD;
	printf("%d\n",ans);
	return 0;
}

```