#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
//const ll mod = 1000000007;
const ll mod998 = 998244353;
const ll intmax = 2147483647;
const ll llmax = 9223372036854775807;
const char sp = ' ';

int N, M;
bitset<300>b[300];
bool f[300];

ll pw(ll x, int y) {
	ll a = 1;
	while (y) {
		if (y & 1)a = a*x%mod998;
		x = x*x%mod998;
		y /= 2;
	}
	return a;
}

int main() {
	cin >> N >> M;
	for (int i = 0; i < N; i++) {
		for (int j = 0; j < M; j++) {
			bool a;
			cin >> a;
			b[i][j] = a;
		}
	}
	for (int i = 0; i < M; i++) {
		for (int j = 0; j < N; j++) {
			if (f[j])continue;
			if (b[j][i]) {
				f[j] = true;
				for (int k = 0; k < N; k++) {
					if (!f[k] && b[k][i]) {
						b[k] ^= b[j];
					}
				}
				break;
			}
		}
	}
	int c = 0;
	for (int i = 0; i < N; i++) {
		if (!f[i])c++;
	}
	cout << (pw(2, N + M - 1) + mod998 - pw(2, c + M - 1)) % mod998 << endl;
}
### Prompt

Please formulate a CPP solution 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>
using namespace std;
typedef long long ll;
//const ll mod = 1000000007;
const ll mod998 = 998244353;
const ll intmax = 2147483647;
const ll llmax = 9223372036854775807;
const char sp = ' ';

int N, M;
bitset<300>b[300];
bool f[300];

ll pw(ll x, int y) {
	ll a = 1;
	while (y) {
		if (y & 1)a = a*x%mod998;
		x = x*x%mod998;
		y /= 2;
	}
	return a;
}

int main() {
	cin >> N >> M;
	for (int i = 0; i < N; i++) {
		for (int j = 0; j < M; j++) {
			bool a;
			cin >> a;
			b[i][j] = a;
		}
	}
	for (int i = 0; i < M; i++) {
		for (int j = 0; j < N; j++) {
			if (f[j])continue;
			if (b[j][i]) {
				f[j] = true;
				for (int k = 0; k < N; k++) {
					if (!f[k] && b[k][i]) {
						b[k] ^= b[j];
					}
				}
				break;
			}
		}
	}
	int c = 0;
	for (int i = 0; i < N; i++) {
		if (!f[i])c++;
	}
	cout << (pw(2, N + M - 1) + mod998 - pw(2, c + M - 1)) % mod998 << endl;
}
```