#include<iostream>
#include<cstdio>
#include<cstdlib>
using namespace std;
const int mod=998244353;
const int N=700;
int n,m,a[N][N];
int od[N],ev[N],bit[N],xxj[N];
int main()
{
	cin>>n>>m;
	for(int i=1;i<=n;i++)
		for(int j=1;j<=m;j++)
			cin>>a[i][j],a[i][j]&=1;
	if(n<m)
	{
		for(int i=1;i<=n;i++)
			for(int j=i+1;j<=m;j++)
				swap(a[i][j],a[j][i]);
		swap(n,m);
	}

	int u=max(n,m);
	od[1]=1;ev[1]=3;
	for(int i=2;i<=u;i++)
	{
		od[i]=(ev[i-1]+3ll*od[i-1]%mod)%mod;
		ev[i]=(od[i-1]+3ll*ev[i-1]%mod)%mod;
	}
	int cnt=0;
	for(int i=1;i<=u;i++)
	{
		int p=i;
		for(int j=i+1;j<=u;j++)
			if(a[i][i]<a[j][i]) p=j;
		if(p!=i) swap(a[p],a[i]);
		if(!a[i][i])
		{
			int fl=0;
			for(int j=i+1;j<=m;j++) fl|=a[i][j];
			if(fl) swap(a[i],a[++u]);
			continue;
		}
		cnt++;
		for(int j=i+1;j<=u;j++)
			if(a[j][i])
				for(int k=i;k<=u;k++)
					a[j][k]^=a[i][k];
	}
/*
	for(int i=1;i<=n;i++)
	{
		for(int j=1;j<=m;j++)
			if(a[i][j])
			{
				if(xxj[j])
					for(int k=j;k<=m;k++)
						a[i][k]^=a[xxj[j]][k];
				else {xxj[j]=i;cnt++;break;}
			}
	}
*/	bit[0]=1;
	for(int i=1;i<=u;i++) bit[i]=2ll*bit[i-1]%mod;
	int bs=1ll*bit[n-cnt]*bit[m-cnt]%mod;
	printf("%lld\n",1ll*od[cnt]*bs%mod);
}

### 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>
using namespace std;
const int mod=998244353;
const int N=700;
int n,m,a[N][N];
int od[N],ev[N],bit[N],xxj[N];
int main()
{
	cin>>n>>m;
	for(int i=1;i<=n;i++)
		for(int j=1;j<=m;j++)
			cin>>a[i][j],a[i][j]&=1;
	if(n<m)
	{
		for(int i=1;i<=n;i++)
			for(int j=i+1;j<=m;j++)
				swap(a[i][j],a[j][i]);
		swap(n,m);
	}

	int u=max(n,m);
	od[1]=1;ev[1]=3;
	for(int i=2;i<=u;i++)
	{
		od[i]=(ev[i-1]+3ll*od[i-1]%mod)%mod;
		ev[i]=(od[i-1]+3ll*ev[i-1]%mod)%mod;
	}
	int cnt=0;
	for(int i=1;i<=u;i++)
	{
		int p=i;
		for(int j=i+1;j<=u;j++)
			if(a[i][i]<a[j][i]) p=j;
		if(p!=i) swap(a[p],a[i]);
		if(!a[i][i])
		{
			int fl=0;
			for(int j=i+1;j<=m;j++) fl|=a[i][j];
			if(fl) swap(a[i],a[++u]);
			continue;
		}
		cnt++;
		for(int j=i+1;j<=u;j++)
			if(a[j][i])
				for(int k=i;k<=u;k++)
					a[j][k]^=a[i][k];
	}
/*
	for(int i=1;i<=n;i++)
	{
		for(int j=1;j<=m;j++)
			if(a[i][j])
			{
				if(xxj[j])
					for(int k=j;k<=m;k++)
						a[i][k]^=a[xxj[j]][k];
				else {xxj[j]=i;cnt++;break;}
			}
	}
*/	bit[0]=1;
	for(int i=1;i<=u;i++) bit[i]=2ll*bit[i-1]%mod;
	int bs=1ll*bit[n-cnt]*bit[m-cnt]%mod;
	printf("%lld\n",1ll*od[cnt]*bs%mod);
}

```