#include<iostream>
#include<string.h>
#include<string>
#include<stdio.h>
#include<algorithm>
#include<math.h>
#include<vector>
#include<queue>
#include<bitset> 
#include<map>
using namespace std;
const int maxd=998244353,N=100000;
const double pi=acos(-1.0);
typedef long long ll;
int n,m,cnt=0;
ll bin[320];
bitset<320> a[320],p[320];

int read()
{
	int x=0,f=1;char ch=getchar();
	while ((ch<'0') || (ch>'9')) {if (ch=='-') f=-1;ch=getchar();}
	while ((ch>='0') && (ch<='9')) {x=x*10+(ch-'0');ch=getchar();}
	return x*f;
}

int main()
{
	n=read();m=read();
	int i,j;
	bin[0]=1;
	for (i=1;i<=300;i++) bin[i]=(bin[i-1]*2)%maxd;
	for (i=1;i<=n;i++)
	{
		for (j=1;j<=m;j++) 
		{
			int tmp=read();
			if (tmp) a[i][j]=1;
		}
	}
	for (i=1;i<=n;i++)
	{
		for (j=1;j<=m;j++)
		{
			if (a[i][j])
			{
				if (p[j][j]) a[i]^=p[j];
				else 
				{
					p[j]=a[i];
					cnt++;
					break;
				}
			}
		}
	}
	ll ans=(((bin[n]-bin[n-cnt])*bin[m-1])%maxd+maxd)%maxd;
	printf("%lld",ans);
	return 0;
}
	

### Prompt

Please create a solution in CPP 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<iostream>
#include<string.h>
#include<string>
#include<stdio.h>
#include<algorithm>
#include<math.h>
#include<vector>
#include<queue>
#include<bitset> 
#include<map>
using namespace std;
const int maxd=998244353,N=100000;
const double pi=acos(-1.0);
typedef long long ll;
int n,m,cnt=0;
ll bin[320];
bitset<320> a[320],p[320];

int read()
{
	int x=0,f=1;char ch=getchar();
	while ((ch<'0') || (ch>'9')) {if (ch=='-') f=-1;ch=getchar();}
	while ((ch>='0') && (ch<='9')) {x=x*10+(ch-'0');ch=getchar();}
	return x*f;
}

int main()
{
	n=read();m=read();
	int i,j;
	bin[0]=1;
	for (i=1;i<=300;i++) bin[i]=(bin[i-1]*2)%maxd;
	for (i=1;i<=n;i++)
	{
		for (j=1;j<=m;j++) 
		{
			int tmp=read();
			if (tmp) a[i][j]=1;
		}
	}
	for (i=1;i<=n;i++)
	{
		for (j=1;j<=m;j++)
		{
			if (a[i][j])
			{
				if (p[j][j]) a[i]^=p[j];
				else 
				{
					p[j]=a[i];
					cnt++;
					break;
				}
			}
		}
	}
	ll ans=(((bin[n]-bin[n-cnt])*bin[m-1])%maxd+maxd)%maxd;
	printf("%lld",ans);
	return 0;
}
	

```