#include <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <cmath>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
#include <complex>
#include <unordered_map>
#include <unordered_set>
#include <random>
#include <cassert>
using namespace std;
typedef long long int ll;
typedef pair<int, int> P;
const ll MOD=998244353;
int main()
{
	int n, m; cin>>n>>m;
	int a[301][301];
	for(int i=0; i<n; i++){
		for(int j=0; j<m; j++) cin>>a[i][j];
	}
	int r=0;
	for(int i=0; i<n; i++){
		int j1=-1;
		for(int j=0; j<m; j++){
			if(a[i][j]){
				j1=j;
				break;
			}
		}
		if(j1==-1) continue;
		r++;
		for(int k=i+1; k<n; k++){
			if(a[k][j1]){
				for(int j=j1; j<m; j++){
					a[k][j]^=a[i][j];
				}
			}
		}
	}
	ll p2[301];
	p2[0]=1;
	for(int i=1; i<=max(n, m); i++) p2[i]=p2[i-1]*2%MOD;
	ll ans=(p2[n]-p2[n-r]+MOD)*p2[m-1]%MOD;
	cout<<ans<<endl;
	return 0;
}
### Prompt

Generate 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 <cstring>
#include <iostream>
#include <string>
#include <cmath>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
#include <complex>
#include <unordered_map>
#include <unordered_set>
#include <random>
#include <cassert>
using namespace std;
typedef long long int ll;
typedef pair<int, int> P;
const ll MOD=998244353;
int main()
{
	int n, m; cin>>n>>m;
	int a[301][301];
	for(int i=0; i<n; i++){
		for(int j=0; j<m; j++) cin>>a[i][j];
	}
	int r=0;
	for(int i=0; i<n; i++){
		int j1=-1;
		for(int j=0; j<m; j++){
			if(a[i][j]){
				j1=j;
				break;
			}
		}
		if(j1==-1) continue;
		r++;
		for(int k=i+1; k<n; k++){
			if(a[k][j1]){
				for(int j=j1; j<m; j++){
					a[k][j]^=a[i][j];
				}
			}
		}
	}
	ll p2[301];
	p2[0]=1;
	for(int i=1; i<=max(n, m); i++) p2[i]=p2[i-1]*2%MOD;
	ll ans=(p2[n]-p2[n-r]+MOD)*p2[m-1]%MOD;
	cout<<ans<<endl;
	return 0;
}
```