#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<functional>
#include<vector>
#include<queue>
#include<stack>
#include<set>
#include<map>
using namespace std;
#define MOD 998244353
#define f(i,n) for(int i=0;i<int(n);i++)
#define N 200000


int main(){
	int n, m, x, z, y;
	vector<int> a[400];
	long long ans = 1;
	long long s = 1;
	scanf("%d %d", &n, &m);
	f(i, n){
		f(j, m){
scanf("%d", &x);
		a[i].push_back(x);
        }
	}
	f(i, n + m - 1){
		ans *= 2;
		ans %= MOD;
	}
	z = 0;
	f(j, m){
		y = -1;
		f(i, n){
			if (a[i][j] == 1)y = i;
		}
		if (y >= 0){
			z++;
			f(i, n){
				if (a[i][j] == 1){
					f(jj, m){
						a[i][jj] = a[i][jj] ^ a[y][jj];
					}
				}
			}
			f(jj, m){
				a[y][jj] = 0;
			}
		}
	}
	s = 1;
	f(i, (n + m-z-1)){
		s *= 2;
		s %= MOD;
	}
	ans = (ans + MOD - s) % MOD;
	printf("%lld\n", ans);



	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<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<functional>
#include<vector>
#include<queue>
#include<stack>
#include<set>
#include<map>
using namespace std;
#define MOD 998244353
#define f(i,n) for(int i=0;i<int(n);i++)
#define N 200000


int main(){
	int n, m, x, z, y;
	vector<int> a[400];
	long long ans = 1;
	long long s = 1;
	scanf("%d %d", &n, &m);
	f(i, n){
		f(j, m){
scanf("%d", &x);
		a[i].push_back(x);
        }
	}
	f(i, n + m - 1){
		ans *= 2;
		ans %= MOD;
	}
	z = 0;
	f(j, m){
		y = -1;
		f(i, n){
			if (a[i][j] == 1)y = i;
		}
		if (y >= 0){
			z++;
			f(i, n){
				if (a[i][j] == 1){
					f(jj, m){
						a[i][jj] = a[i][jj] ^ a[y][jj];
					}
				}
			}
			f(jj, m){
				a[y][jj] = 0;
			}
		}
	}
	s = 1;
	f(i, (n + m-z-1)){
		s *= 2;
		s %= MOD;
	}
	ans = (ans + MOD - s) % MOD;
	printf("%lld\n", ans);



	return 0;
}
```