#include<bits/stdc++.h>
#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<vector>
#include<set>
#include<map>
#include<bitset>
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define IL inline
using namespace std;
typedef long long LL;
typedef unsigned int U;
typedef unsigned long long LLU;
typedef pair<int,int> PII;
typedef long double LD;
IL LL read()
{
	LL 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<<1)+(x<<3)+(ch^48);ch=getchar();}
	return x*f;
}
#define io read()
const int mod=998244353;
IL LL ksm(LL x,int y)
{
	LL tmp=1;
	while(y){
		if(y&1)	tmp=tmp*x%mod;
		x=x*x%mod;
		y>>=1;	
	}
	return tmp;
}
IL void upd(int &x,int y)
{
	x+=y;
	if(x>=mod)	x-=mod;	
}
const int N=308;
int n,m;
bitset<N> a[N];
int ans;
IL void gauss()
{
	int i,j;
	for(i=1,j=1;j<=m;++j){
		if(a[i][j]==0){
			int t;
			for(t=i+1;t<=n;++t){
				if(a[t][j])	break;
			}
			if(t>n)	continue;
			swap(a[t],a[i]);
		}
		for(int t=i+1;t<=n;++t){
			if(a[t][j])	a[t]^=a[i];	
		}
		++i;
	}
	//(i-1)个主元 
	for(int t=i+1;t<=n;++t){
		if(a[t][m+1]){
			ans=0;
			return;
		}
	}
	ans=ksm(2,m-i+1);
}
int main()
{
	n=io;m=io;
	for(int i=1;i<=n;++i){
		for(int j=1;j<=m;++j){
			a[i][j]=io;	
		}
	}
	gauss();
	printf("%lld",(ksm(2,n+m-1)-ksm(2,n-1)*ans%mod+mod)%mod);
	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<bits/stdc++.h>
#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<vector>
#include<set>
#include<map>
#include<bitset>
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define IL inline
using namespace std;
typedef long long LL;
typedef unsigned int U;
typedef unsigned long long LLU;
typedef pair<int,int> PII;
typedef long double LD;
IL LL read()
{
	LL 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<<1)+(x<<3)+(ch^48);ch=getchar();}
	return x*f;
}
#define io read()
const int mod=998244353;
IL LL ksm(LL x,int y)
{
	LL tmp=1;
	while(y){
		if(y&1)	tmp=tmp*x%mod;
		x=x*x%mod;
		y>>=1;	
	}
	return tmp;
}
IL void upd(int &x,int y)
{
	x+=y;
	if(x>=mod)	x-=mod;	
}
const int N=308;
int n,m;
bitset<N> a[N];
int ans;
IL void gauss()
{
	int i,j;
	for(i=1,j=1;j<=m;++j){
		if(a[i][j]==0){
			int t;
			for(t=i+1;t<=n;++t){
				if(a[t][j])	break;
			}
			if(t>n)	continue;
			swap(a[t],a[i]);
		}
		for(int t=i+1;t<=n;++t){
			if(a[t][j])	a[t]^=a[i];	
		}
		++i;
	}
	//(i-1)个主元 
	for(int t=i+1;t<=n;++t){
		if(a[t][m+1]){
			ans=0;
			return;
		}
	}
	ans=ksm(2,m-i+1);
}
int main()
{
	n=io;m=io;
	for(int i=1;i<=n;++i){
		for(int j=1;j<=m;++j){
			a[i][j]=io;	
		}
	}
	gauss();
	printf("%lld",(ksm(2,n+m-1)-ksm(2,n-1)*ans%mod+mod)%mod);
	return 0;
}

```