#include <iostream>
#define llint long long
#define mod 998244353

using namespace std;

llint h, w;
int a[305][305];

void swapRows(int mat[305][305], int i, int j, int w)
{
	for(int k = 0; k < w; k++) swap(mat[i][k], mat[j][k]);
}

void GaussianElimination(int mat[305][305], int w, int h)
{
	int r = 0;
	for(int i = 0; i < w && r < h; i++){
		if(mat[i][r] == 0){
			int max_val = 0, max_j;
			for(int j = r+1; j < h; j++){
				if(mat[j][i] > max_val){
					max_val = mat[j][i];
					max_j = j;
				}
			}
			if(max_val == 0) goto end;
			swapRows(mat, r, max_j, w);
		}
		
		for(int j = 0; j < h; j++){
			if(j == r) continue;
			if(mat[j][i] == 0) continue;
			for(int k = 0; k <= w; k++){
				mat[j][k] ^= mat[r][k];
			}
		}
		r++;
		end:;
	}
}

int main(void)
{
	cin >> h >> w;
	for(int i = 0; i < h; i++){
		for(int j = 0; j < w; j++){
			cin >> a[i][j];
		}
	}
	
	GaussianElimination(a, w, h);
	
	llint rank = 0;
	for(int i = 0; i < h; i++){
		bool flag = false;
		for(int j = 0; j < w; j++) if(a[i][j]) flag = true;
		if(flag) rank++;
	}
	
	llint nsize = 1, dsize = 1;
	for(int i = 0; i < h-rank; i++) nsize *= 2, nsize %= mod;
	for(int i = 0; i < h; i++) dsize *= 2, dsize %= mod;
	llint ans = (dsize - nsize + mod) % mod;
	for(int i = 0; i < w-1; i++) ans *= 2, ans %= mod;
	
	cout << ans << endl;
	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 <iostream>
#define llint long long
#define mod 998244353

using namespace std;

llint h, w;
int a[305][305];

void swapRows(int mat[305][305], int i, int j, int w)
{
	for(int k = 0; k < w; k++) swap(mat[i][k], mat[j][k]);
}

void GaussianElimination(int mat[305][305], int w, int h)
{
	int r = 0;
	for(int i = 0; i < w && r < h; i++){
		if(mat[i][r] == 0){
			int max_val = 0, max_j;
			for(int j = r+1; j < h; j++){
				if(mat[j][i] > max_val){
					max_val = mat[j][i];
					max_j = j;
				}
			}
			if(max_val == 0) goto end;
			swapRows(mat, r, max_j, w);
		}
		
		for(int j = 0; j < h; j++){
			if(j == r) continue;
			if(mat[j][i] == 0) continue;
			for(int k = 0; k <= w; k++){
				mat[j][k] ^= mat[r][k];
			}
		}
		r++;
		end:;
	}
}

int main(void)
{
	cin >> h >> w;
	for(int i = 0; i < h; i++){
		for(int j = 0; j < w; j++){
			cin >> a[i][j];
		}
	}
	
	GaussianElimination(a, w, h);
	
	llint rank = 0;
	for(int i = 0; i < h; i++){
		bool flag = false;
		for(int j = 0; j < w; j++) if(a[i][j]) flag = true;
		if(flag) rank++;
	}
	
	llint nsize = 1, dsize = 1;
	for(int i = 0; i < h-rank; i++) nsize *= 2, nsize %= mod;
	for(int i = 0; i < h; i++) dsize *= 2, dsize %= mod;
	llint ans = (dsize - nsize + mod) % mod;
	for(int i = 0; i < w-1; i++) ans *= 2, ans %= mod;
	
	cout << ans << endl;
	return 0;
}
```