#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int H, W;
long long mod = 998244353;
vector<int> A[309];

int main() {
	cin >> H >> W;
	for (int i = 0; i < H; i++) {
		A[i].resize(W, 0);
		for (int j = 0; j < W; j++) cin >> A[i][j];
	}
	sort(A, A + H);

	for (int i = 0; i < W; i++) {
		int pos = 0;
		for (int j = 0; j < H; j++) {
			int cnt = 0; for (int k = 0; k < i; k++) { if (A[j][k] == 1) cnt++; }
			if (cnt == 0) { pos = j; }
		}
		for (int j = pos - 1; j >= 0; j--) {
			if (A[j][i] == 0) continue;
			for (int k = 0; k < W; k++) A[j][k] ^= A[pos][k];
		}
		sort(A, A + H);
	}

	vector<int> ZERO(W, 0);
	long long v = 1;
	for (int i = 0; i < H; i++) {
		if (A[i] == ZERO) { v *= 2; v %= mod; }
	}
	long long p = 1; for (int i = 0; i < H; i++) { p *= 2; p %= mod; }
	long long q = 1; for (int i = 0; i < W; i++) { q *= 2; q %= mod; }
	long long r = (p - v + mod)*q%mod;
	if (r % 2 == 1) r += mod; r /= 2;
	cout << r << 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 <vector>
#include <algorithm>
using namespace std;

int H, W;
long long mod = 998244353;
vector<int> A[309];

int main() {
	cin >> H >> W;
	for (int i = 0; i < H; i++) {
		A[i].resize(W, 0);
		for (int j = 0; j < W; j++) cin >> A[i][j];
	}
	sort(A, A + H);

	for (int i = 0; i < W; i++) {
		int pos = 0;
		for (int j = 0; j < H; j++) {
			int cnt = 0; for (int k = 0; k < i; k++) { if (A[j][k] == 1) cnt++; }
			if (cnt == 0) { pos = j; }
		}
		for (int j = pos - 1; j >= 0; j--) {
			if (A[j][i] == 0) continue;
			for (int k = 0; k < W; k++) A[j][k] ^= A[pos][k];
		}
		sort(A, A + H);
	}

	vector<int> ZERO(W, 0);
	long long v = 1;
	for (int i = 0; i < H; i++) {
		if (A[i] == ZERO) { v *= 2; v %= mod; }
	}
	long long p = 1; for (int i = 0; i < H; i++) { p *= 2; p %= mod; }
	long long q = 1; for (int i = 0; i < W; i++) { q *= 2; q %= mod; }
	long long r = (p - v + mod)*q%mod;
	if (r % 2 == 1) r += mod; r /= 2;
	cout << r << endl;
	return 0;
}
```