#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
const ll MOD = 998244353;
const ll INF = 1LL << 60;
const double PI = 3.141592653589793238;
const double EPS = 1e-10;
ll mod_pow(ll a, ll b) {
	if (b == 0) return 1;
	if (b % 2 == 0) {
		ll x = mod_pow(a, b / 2);
		return (x*x) % MOD;
	}
	return (a*mod_pow(a, b - 1)) % MOD;
}
int a[300][300];
int main() {
	int N, M;
	cin >> N >> M;
	for (int i = 0; i < N; i++) {
		for (int j = 0; j < M; j++) {
			cin >> a[i][j];
		}
	}
	int r = 0;
	for (int i = 0; i < N; i++) {
		int idx = -1, l = -1;
		for (int j = i; j < N; j++) {
			int k;
			for (k = 0; k < M; k++) {
				if (a[j][k]) break;
			}
			if (k < M) {
				if (idx == -1 || l > k) idx = j, l = k;
			}
		}
		if (idx == -1) break;
		r++;
		for (int j = 0; j < M; j++) {
			swap(a[i][j], a[idx][j]);
		}
		for (int j = 0; j < N; j++) {
			if (i == j || a[j][l] == 0) continue;
			for (int k = 0; k < M; k++) {
				a[j][k] ^= a[i][k];
			}
		}
	}
	ll ans = mod_pow(2, N + M - 1);
	(ans += MOD - mod_pow(2, N + M - r - 1)) %= MOD;
	cout << ans << endl;
}
### Prompt

Develop a solution in Cpp 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;
typedef long long ll;
const ll MOD = 998244353;
const ll INF = 1LL << 60;
const double PI = 3.141592653589793238;
const double EPS = 1e-10;
ll mod_pow(ll a, ll b) {
	if (b == 0) return 1;
	if (b % 2 == 0) {
		ll x = mod_pow(a, b / 2);
		return (x*x) % MOD;
	}
	return (a*mod_pow(a, b - 1)) % MOD;
}
int a[300][300];
int main() {
	int N, M;
	cin >> N >> M;
	for (int i = 0; i < N; i++) {
		for (int j = 0; j < M; j++) {
			cin >> a[i][j];
		}
	}
	int r = 0;
	for (int i = 0; i < N; i++) {
		int idx = -1, l = -1;
		for (int j = i; j < N; j++) {
			int k;
			for (k = 0; k < M; k++) {
				if (a[j][k]) break;
			}
			if (k < M) {
				if (idx == -1 || l > k) idx = j, l = k;
			}
		}
		if (idx == -1) break;
		r++;
		for (int j = 0; j < M; j++) {
			swap(a[i][j], a[idx][j]);
		}
		for (int j = 0; j < N; j++) {
			if (i == j || a[j][l] == 0) continue;
			for (int k = 0; k < M; k++) {
				a[j][k] ^= a[i][k];
			}
		}
	}
	ll ans = mod_pow(2, N + M - 1);
	(ans += MOD - mod_pow(2, N + M - r - 1)) %= MOD;
	cout << ans << endl;
}
```