#include <bits/stdc++.h>
#define PII pair<int, int>
#define LL long long
using namespace std;
const int MAXN = 305;
const int INF = (LL)1e9 + 5;
const int MOD = 998244353;

int N, M, C[MAXN][MAXN], pw[MAXN];
vector<bitset<MAXN>> a;

void gaussian(vector<bitset<MAXN>> &a) {
	int pos = 0;
	for (int j = 0; j < M && pos < N; j++) {
		bool go = false;
		for (int i = pos; i < N; i++) {
			if (a[i][j]) {
				swap(a[i], a[pos]);
				go = true;
				break;
			}
		}
		if (!go) continue;
		for (int i = pos + 1; i < N; i++) {
			if (a[i][j]) {
				a[i] ^= a[pos];
			}
		}
		pos++;
	}
}

int qpow(int a, int pw) {
	int res = 1;
	while (pw) {
		if (pw & 1) res = (LL) res * a % MOD;
		pw >>= 1;
		a = (LL) a * a % MOD;
	}
	return res;
}

int main() {
	ios_base::sync_with_stdio(0); cin.tie(0);

	for (int n = 1; n < MAXN; n++) {
		C[n][0] = C[n][n] = 1;
		for (int k = 1; k < n; k++) {
			C[n][k] = C[n - 1][k] + C[n - 1][k - 1];
			C[n][k] %= MOD;
		}
	}

	cin >> N >> M;
	a.resize(N);
	for (int i = 0; i < N; i++) {
		for (int j = 0; j < M; j++) {
			int x;
			cin >> x;
			a[i][j] = x;
		}
 	}

	int r = 0;
	gaussian(a);
	for (int i = 0; i < N; i++) {
		if (a[i].any()) {
			r++;
		}
	}

	int ans = 0;
	assert(r <= N && r <= M);
	for (int i = 1; i <= r; i += 2) {
		int add = (LL) C[r][i] * qpow(3, r - i) % MOD * qpow(2, N + M - r - r) % MOD;
		ans = (ans + add) % MOD;
	}
	
	cout << ans << '\n';

	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 <bits/stdc++.h>
#define PII pair<int, int>
#define LL long long
using namespace std;
const int MAXN = 305;
const int INF = (LL)1e9 + 5;
const int MOD = 998244353;

int N, M, C[MAXN][MAXN], pw[MAXN];
vector<bitset<MAXN>> a;

void gaussian(vector<bitset<MAXN>> &a) {
	int pos = 0;
	for (int j = 0; j < M && pos < N; j++) {
		bool go = false;
		for (int i = pos; i < N; i++) {
			if (a[i][j]) {
				swap(a[i], a[pos]);
				go = true;
				break;
			}
		}
		if (!go) continue;
		for (int i = pos + 1; i < N; i++) {
			if (a[i][j]) {
				a[i] ^= a[pos];
			}
		}
		pos++;
	}
}

int qpow(int a, int pw) {
	int res = 1;
	while (pw) {
		if (pw & 1) res = (LL) res * a % MOD;
		pw >>= 1;
		a = (LL) a * a % MOD;
	}
	return res;
}

int main() {
	ios_base::sync_with_stdio(0); cin.tie(0);

	for (int n = 1; n < MAXN; n++) {
		C[n][0] = C[n][n] = 1;
		for (int k = 1; k < n; k++) {
			C[n][k] = C[n - 1][k] + C[n - 1][k - 1];
			C[n][k] %= MOD;
		}
	}

	cin >> N >> M;
	a.resize(N);
	for (int i = 0; i < N; i++) {
		for (int j = 0; j < M; j++) {
			int x;
			cin >> x;
			a[i][j] = x;
		}
 	}

	int r = 0;
	gaussian(a);
	for (int i = 0; i < N; i++) {
		if (a[i].any()) {
			r++;
		}
	}

	int ans = 0;
	assert(r <= N && r <= M);
	for (int i = 1; i <= r; i += 2) {
		int add = (LL) C[r][i] * qpow(3, r - i) % MOD * qpow(2, N + M - r - r) % MOD;
		ans = (ans + add) % MOD;
	}
	
	cout << ans << '\n';

	return 0;
}
```