#include<cstdio>
#include<algorithm>
#include<cstring>
#include<iostream>
#include<cmath>
#include<cctype>
#include<set>
#include<queue>
#include<vector>
#include<map>
#include<bitset>
using namespace std;
typedef long long LL;

inline int read() {
	int x=0,f=1;char ch=getchar();for(;!isdigit(ch);ch=getchar())if(ch=='-')f=-1;
	for(;isdigit(ch);ch=getchar())x=x*10+ch-'0';return x*f;
}

const int N = 305, mod = 998244353;
bitset<N>a[N], b[N];

int ksm(int a,int b) {
	int res = 1;
	while (b) {
		if (b & 1) res = 1ll * res * a % mod;
		a = 1ll * a * a % mod;
		b >>= 1;
	}
	return res;
}

int main() {
	int n = read(), m = read(), cnt = 0;
	for (int i = 1; i <= n; ++i) 
		for (int j = 1; j <= m; ++j) a[i][j] = read();
	for (int i = 1; i <= n; ++i) 
		for (int j = 1; j <= m; ++j) 
			if (a[i][j]) {
				if (!b[j][j]) {
					b[j] = a[i];
					cnt ++;
					break;
				}
				else {
					a[i] ^= b[j];
				}
			}
	cout << 1ll * (ksm(2, n) - ksm(2, n - cnt) + mod) % mod * ksm(2, m - 1) % mod;
	return 0;
}
### Prompt

Create a solution in cpp for 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<algorithm>
#include<cstring>
#include<iostream>
#include<cmath>
#include<cctype>
#include<set>
#include<queue>
#include<vector>
#include<map>
#include<bitset>
using namespace std;
typedef long long LL;

inline int read() {
	int x=0,f=1;char ch=getchar();for(;!isdigit(ch);ch=getchar())if(ch=='-')f=-1;
	for(;isdigit(ch);ch=getchar())x=x*10+ch-'0';return x*f;
}

const int N = 305, mod = 998244353;
bitset<N>a[N], b[N];

int ksm(int a,int b) {
	int res = 1;
	while (b) {
		if (b & 1) res = 1ll * res * a % mod;
		a = 1ll * a * a % mod;
		b >>= 1;
	}
	return res;
}

int main() {
	int n = read(), m = read(), cnt = 0;
	for (int i = 1; i <= n; ++i) 
		for (int j = 1; j <= m; ++j) a[i][j] = read();
	for (int i = 1; i <= n; ++i) 
		for (int j = 1; j <= m; ++j) 
			if (a[i][j]) {
				if (!b[j][j]) {
					b[j] = a[i];
					cnt ++;
					break;
				}
				else {
					a[i] ^= b[j];
				}
			}
	cout << 1ll * (ksm(2, n) - ksm(2, n - cnt) + mod) % mod * ksm(2, m - 1) % mod;
	return 0;
}
```