#include <bits/stdc++.h>
using namespace std;
//#define che
#define debug(...) fprintf(stderr,__VA_ARGS__)
#define MK make_pair
#define PB push_back
#define fi first
#define se second

typedef long long LL;
typedef pair<int, int> PII;
const int N=303;
const LL MOD= 998244353;
typedef bitset<N> bs;

bs a[N];
LL pw[N];
int n,m;



int main(){
	#ifdef che
	freopen("input.txt","rt",stdin);
	freopen("output.txt","wt",stdout);
	#endif
	scanf("%d%d", &n, &m);
	pw[0]=1;
	for (int i=1; i<N; ++i) pw[i]=(pw[i-1]<<1)%MOD;
	for (int i=0,x; i<n; ++i)
		for (int j=0; j<m; ++j){
			scanf("%d", &x);
			if ( x) a[i].flip(j);
		}
	
	for (int i=0,j=0; i<n && j<m; ++j){
		bool flag=false;
		for (int k=i; k<n; ++k)
			if ( a[k].test(j)){
				swap(a[i],a[k]);
				flag= true;break;
			}
		if ( flag){
			for (int k=i+1; k<n; ++k)
				if ( a[k].test(j)) a[k]^=a[i];
			++i;
		}
	}
	int fr=0;// free row
	for (int i=0; i<n; ++i) if ( a[i].count()==0) ++fr;
	LL ans= (pw[n]-pw[fr]+MOD)%MOD;
	ans=ans*pw[m-1]%MOD;
	printf("%lld\n", ans);
	return 0;
}
### Prompt

Please provide a CPP coded solution to the problem described below:

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;
//#define che
#define debug(...) fprintf(stderr,__VA_ARGS__)
#define MK make_pair
#define PB push_back
#define fi first
#define se second

typedef long long LL;
typedef pair<int, int> PII;
const int N=303;
const LL MOD= 998244353;
typedef bitset<N> bs;

bs a[N];
LL pw[N];
int n,m;



int main(){
	#ifdef che
	freopen("input.txt","rt",stdin);
	freopen("output.txt","wt",stdout);
	#endif
	scanf("%d%d", &n, &m);
	pw[0]=1;
	for (int i=1; i<N; ++i) pw[i]=(pw[i-1]<<1)%MOD;
	for (int i=0,x; i<n; ++i)
		for (int j=0; j<m; ++j){
			scanf("%d", &x);
			if ( x) a[i].flip(j);
		}
	
	for (int i=0,j=0; i<n && j<m; ++j){
		bool flag=false;
		for (int k=i; k<n; ++k)
			if ( a[k].test(j)){
				swap(a[i],a[k]);
				flag= true;break;
			}
		if ( flag){
			for (int k=i+1; k<n; ++k)
				if ( a[k].test(j)) a[k]^=a[i];
			++i;
		}
	}
	int fr=0;// free row
	for (int i=0; i<n; ++i) if ( a[i].count()==0) ++fr;
	LL ans= (pw[n]-pw[fr]+MOD)%MOD;
	ans=ans*pw[m-1]%MOD;
	printf("%lld\n", ans);
	return 0;
}
```