#include<cstdio>
#include<algorithm>
#include<cstring>
#include<bitset>
using namespace std;
int gi(){
	int x=0,w=1;char ch=getchar();
	while((ch<'0'||ch>'9')&&ch!='-')ch=getchar();
	if(ch=='-')w=0,ch=getchar();
	while(ch>='0'&&ch<='9')x=(x<<3)+(x<<1)+ch-'0',ch=getchar();
	return w?x:-x;
}
const int N=305;
const int mod=998244353;
int n,m,r,bin[N];bitset<N>p[N];
void insert(bitset<N>x){
	for(int j=1;j<=m;++j)
		if(x[j])
			if(p[j][j])x^=p[j];
			else{p[j]=x;++r;return;}
}
int main(){
	n=gi();m=gi();
	for(int i=1;i<=n;++i){
		bitset<N>x;x.reset();
		for(int j=1;j<=m;++j)x[j]=gi();
		insert(x);
	}
	for(int i=bin[0]=1;i<N;++i)bin[i]=(bin[i-1]<<1)%mod;
	printf("%lld\n",1ll*(bin[n]-bin[n-r]+mod)*bin[m-1]%mod);
	return 0;
}

### Prompt

Your challenge is to write a cpp solution 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<cstdio>
#include<algorithm>
#include<cstring>
#include<bitset>
using namespace std;
int gi(){
	int x=0,w=1;char ch=getchar();
	while((ch<'0'||ch>'9')&&ch!='-')ch=getchar();
	if(ch=='-')w=0,ch=getchar();
	while(ch>='0'&&ch<='9')x=(x<<3)+(x<<1)+ch-'0',ch=getchar();
	return w?x:-x;
}
const int N=305;
const int mod=998244353;
int n,m,r,bin[N];bitset<N>p[N];
void insert(bitset<N>x){
	for(int j=1;j<=m;++j)
		if(x[j])
			if(p[j][j])x^=p[j];
			else{p[j]=x;++r;return;}
}
int main(){
	n=gi();m=gi();
	for(int i=1;i<=n;++i){
		bitset<N>x;x.reset();
		for(int j=1;j<=m;++j)x[j]=gi();
		insert(x);
	}
	for(int i=bin[0]=1;i<N;++i)bin[i]=(bin[i-1]<<1)%mod;
	printf("%lld\n",1ll*(bin[n]-bin[n-r]+mod)*bin[m-1]%mod);
	return 0;
}

```