#include<cmath>
#include<cstdio>
#include<cstring>
#include<bitset>
#include<algorithm>
#define gt getchar()
#define ll long long
#define File(s) freopen(s".in","r",stdin),freopen(s".out","w",stdout)
inline int in()
{
	int k=0;char ch=gt;
	while(ch<'-')ch=gt;
	while(ch>'-')k=k*10+ch-'0',ch=gt;
	return k;
}
const int N=2e5+5,YL=998244353;
inline int ksm(int a,int k){int r=1;while(k){if(k&1)r=1ll*r*a%YL;a=1ll*a*a%YL,k>>=1;}return r;}
std::bitset<305>a[305],now;
int n,m;
inline void insert(std::bitset<305> x)
{
	for(int i=m;i>=1;--i)
		if(x[i])
		{
			if(a[i][i])x^=a[i];
			else {a[i]=x;break;}
		}
}
int main()
{
	n=in(),m=in();int r=0;
	for(int i=1;i<=n;++i)
	{
		now.reset();
		for(int j=1;j<=m;++j)now[j]=in();
		insert(now);
	}
	for(int i=1;i<=m;++i)r+=(a[i].count()!=0);
	int ans=ksm(2,n)-ksm(2,n-r);if(ans<0)ans+=YL;
	ans=1ll*ans*ksm(2,m-1)%YL;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<cmath>
#include<cstdio>
#include<cstring>
#include<bitset>
#include<algorithm>
#define gt getchar()
#define ll long long
#define File(s) freopen(s".in","r",stdin),freopen(s".out","w",stdout)
inline int in()
{
	int k=0;char ch=gt;
	while(ch<'-')ch=gt;
	while(ch>'-')k=k*10+ch-'0',ch=gt;
	return k;
}
const int N=2e5+5,YL=998244353;
inline int ksm(int a,int k){int r=1;while(k){if(k&1)r=1ll*r*a%YL;a=1ll*a*a%YL,k>>=1;}return r;}
std::bitset<305>a[305],now;
int n,m;
inline void insert(std::bitset<305> x)
{
	for(int i=m;i>=1;--i)
		if(x[i])
		{
			if(a[i][i])x^=a[i];
			else {a[i]=x;break;}
		}
}
int main()
{
	n=in(),m=in();int r=0;
	for(int i=1;i<=n;++i)
	{
		now.reset();
		for(int j=1;j<=m;++j)now[j]=in();
		insert(now);
	}
	for(int i=1;i<=m;++i)r+=(a[i].count()!=0);
	int ans=ksm(2,n)-ksm(2,n-r);if(ans<0)ans+=YL;
	ans=1ll*ans*ksm(2,m-1)%YL;printf("%d\n",ans);
	return 0;
}

```