#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cstring>
#include <algorithm>
using namespace std;
const int maxn = 310;
const long long mod = 998244353;
long long power(long long x, long long k)
{
	long long ans = 1;
	while(k)
	{
		if(k & 1)
			(ans *= x) %= mod;
		k >>= 1;
		(x *= x) %= mod;
	}
	return ans;
}
int n, m;
bool v[maxn][maxn];
bool base[maxn][maxn] = {0};
int cnt = 0;
void out()
{
	cout << cnt << endl;
	for(int i = 1; i <= n; i ++)
	{
		for(int j = 1; j <= m; j ++)
			cout << base[i][j] << " ";
		cout << endl;
	}
}
void insert(int x)
{
	for(int i = 1; i <= m; i ++)
	{
		if(v[x][i])
		{
			if(!base[i][i])
			{
				for(int j = i; j <= m; j ++)
					base[i][j] = v[x][j];
				cnt ++;
				return ;
			}
			else
			{
				for(int j = i; j <= m; j ++)
					v[x][j] ^= base[i][j];
			}
		}
	}
}
int main()
{
	std::ios::sync_with_stdio(false);
	cin >> n >> m;
	for(int i = 1; i <= n; i ++)
	{
		for(int j = 1; j <= m; j ++)
			cin >> v[i][j];
		insert(i);
	}
	
	cout << (power(2, n) - power(2, n - cnt) + mod) * power(2, m - 1) % mod << endl;
	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 <iostream>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cstring>
#include <algorithm>
using namespace std;
const int maxn = 310;
const long long mod = 998244353;
long long power(long long x, long long k)
{
	long long ans = 1;
	while(k)
	{
		if(k & 1)
			(ans *= x) %= mod;
		k >>= 1;
		(x *= x) %= mod;
	}
	return ans;
}
int n, m;
bool v[maxn][maxn];
bool base[maxn][maxn] = {0};
int cnt = 0;
void out()
{
	cout << cnt << endl;
	for(int i = 1; i <= n; i ++)
	{
		for(int j = 1; j <= m; j ++)
			cout << base[i][j] << " ";
		cout << endl;
	}
}
void insert(int x)
{
	for(int i = 1; i <= m; i ++)
	{
		if(v[x][i])
		{
			if(!base[i][i])
			{
				for(int j = i; j <= m; j ++)
					base[i][j] = v[x][j];
				cnt ++;
				return ;
			}
			else
			{
				for(int j = i; j <= m; j ++)
					v[x][j] ^= base[i][j];
			}
		}
	}
}
int main()
{
	std::ios::sync_with_stdio(false);
	cin >> n >> m;
	for(int i = 1; i <= n; i ++)
	{
		for(int j = 1; j <= m; j ++)
			cin >> v[i][j];
		insert(i);
	}
	
	cout << (power(2, n) - power(2, n - cnt) + mod) * power(2, m - 1) % mod << endl;
	return 0;
}
```