#include <bits/stdc++.h>
using namespace std;

#define N 1005
#define MP make_pair
typedef long long LL;
const int mod = 998244353;

int n, m;
int a[500][500];

int main()
{
	//freopen("in.txt", "r", stdin);
	
	scanf("%d%d", &n, &m);
	for (int i = 1; i <= n; ++i)
		for (int j = 1; j <= m; ++j)
			scanf("%d", &a[j][i]);
	
	swap(n, m); 
	int r = 1;
	for (int i = 1; i <= m; ++i)
	{
		int k = -1;
		for (int j = r; j <= n; ++j)
			if (a[j][i]) k = j;
		
		if (k == -1) continue;
		for (int j = 1; j <= m; ++j)
			swap(a[k][j], a[r][j]);
		for (int j = r + 1; j <= n; ++j)
		{
			if (!a[j][i]) continue;
			for (int l = i; l <= m; ++l)
				a[j][l] ^= a[r][l];
		}
		++r;
	}
	int t = 1;
	r--; r = m - r;
	while (r--) t = t * 2 % mod;
	
	LL ans = 1;
	int t1 = 1, t2 = 1;
	for (int i = 1; i <= m; ++i)
		t1 = t1 * 2 % mod;
	for (int i = 1; i < n; ++i)
		t2 = t2 * 2 % mod;
	
	ans = 1LL * (t1 - t) * t2 % mod;
	if (ans < 0) ans += mod;
	cout << ans << endl;
	
	
	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 N 1005
#define MP make_pair
typedef long long LL;
const int mod = 998244353;

int n, m;
int a[500][500];

int main()
{
	//freopen("in.txt", "r", stdin);
	
	scanf("%d%d", &n, &m);
	for (int i = 1; i <= n; ++i)
		for (int j = 1; j <= m; ++j)
			scanf("%d", &a[j][i]);
	
	swap(n, m); 
	int r = 1;
	for (int i = 1; i <= m; ++i)
	{
		int k = -1;
		for (int j = r; j <= n; ++j)
			if (a[j][i]) k = j;
		
		if (k == -1) continue;
		for (int j = 1; j <= m; ++j)
			swap(a[k][j], a[r][j]);
		for (int j = r + 1; j <= n; ++j)
		{
			if (!a[j][i]) continue;
			for (int l = i; l <= m; ++l)
				a[j][l] ^= a[r][l];
		}
		++r;
	}
	int t = 1;
	r--; r = m - r;
	while (r--) t = t * 2 % mod;
	
	LL ans = 1;
	int t1 = 1, t2 = 1;
	for (int i = 1; i <= m; ++i)
		t1 = t1 * 2 % mod;
	for (int i = 1; i < n; ++i)
		t2 = t2 * 2 % mod;
	
	ans = 1LL * (t1 - t) * t2 % mod;
	if (ans < 0) ans += mod;
	cout << ans << endl;
	
	
	return 0;
}
```