#include <bits/stdc++.h>
using namespace std;
bitset<305> a[305],b;
int n,m,i,j,pw[305],mod=998244353,cnt;
int main()
{
	scanf("%d%d",&n,&m);
	pw[0]=1;
	for (i=1;i<=300;i++) pw[i]=pw[i-1]*2ll%mod;
	for (i=1;i<=n;i++)
	{
		b.reset();
		for (j=1;j<=m;j++)
		{
			int x;
			scanf("%d",&x);
			b[j]=x;
		}
		for (j=m;j>=1;j--)
		{
			if (b[j])
			{
				if (a[j].any())
				{
					b^=a[j];
				}
				else
				{
					a[j]=b;
					break;
				}
			}
		}
		if (j<1) cnt++;
	}
	cout<<((1ll*(pw[n]-pw[cnt])*pw[m-1]%mod+mod)%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 <bits/stdc++.h>
using namespace std;
bitset<305> a[305],b;
int n,m,i,j,pw[305],mod=998244353,cnt;
int main()
{
	scanf("%d%d",&n,&m);
	pw[0]=1;
	for (i=1;i<=300;i++) pw[i]=pw[i-1]*2ll%mod;
	for (i=1;i<=n;i++)
	{
		b.reset();
		for (j=1;j<=m;j++)
		{
			int x;
			scanf("%d",&x);
			b[j]=x;
		}
		for (j=m;j>=1;j--)
		{
			if (b[j])
			{
				if (a[j].any())
				{
					b^=a[j];
				}
				else
				{
					a[j]=b;
					break;
				}
			}
		}
		if (j<1) cnt++;
	}
	cout<<((1ll*(pw[n]-pw[cnt])*pw[m-1]%mod+mod)%mod);
	return 0;
}
```