#include <iostream>
#include <string>
#include <functional>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <vector>
#include <map>
#include <set>
#include <bitset>
#include <string>
#include <cstring>
#include <algorithm>

#define range(i, l, r) for (int i = (l); i <= (r); i++)

using i64 = int64_t;

using namespace std;

const int N = 500;

const i64 modp = 998244353;

int n, m, a[N][N];

void swap_row(int x, int y) {
	static int t[N];
	memcpy(t, a[x], sizeof(int) * m);
	memcpy(a[x], a[y], sizeof(int) * m);
	memcpy(a[y], t, sizeof(int) * m);
}

void xor_row(int x, int y) {
	range(i, 0, m - 1) a[x][i] ^= a[y][i];
}

// return rank
int gaussian(int x, int y) {
	if (x >= n) return n;
	if (y >= m) {
		return x;
	}
	int p = n;
	range(i, x, n - 1) if (a[i][y] == 1) { p = i; break; }
	if (p >= n) {
		return gaussian(x, y + 1);
	} else {
		if (x != p) swap_row(x, p);
		range(i, x + 1, n - 1) {
			if (a[i][y] == 0) continue;
			xor_row(i, x);
		}
		return gaussian(x + 1, y + 1);
	}
}

i64 qpow(i64 a, i64 b) {
	if (b == 0) return 1;
	i64 t = qpow(a, b >> 1ll);
	t = t * t % modp;
	if (b & 1) t = t * a % modp;
	return t;
}

int main() {
	cin >> n >> m;
	range(i, 0, n - 1) range(j, 0, m - 1) scanf("%d", &a[i][j]);
	int r = gaussian(0, 0);
	i64 ans = qpow(2, m - 1) * ((qpow(2, n) - qpow(2, n - r)) % modp) % modp;
	ans = (ans + modp) % modp;
	cout << ans << endl;
    return 0;
}
### Prompt

Generate 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 <iostream>
#include <string>
#include <functional>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <vector>
#include <map>
#include <set>
#include <bitset>
#include <string>
#include <cstring>
#include <algorithm>

#define range(i, l, r) for (int i = (l); i <= (r); i++)

using i64 = int64_t;

using namespace std;

const int N = 500;

const i64 modp = 998244353;

int n, m, a[N][N];

void swap_row(int x, int y) {
	static int t[N];
	memcpy(t, a[x], sizeof(int) * m);
	memcpy(a[x], a[y], sizeof(int) * m);
	memcpy(a[y], t, sizeof(int) * m);
}

void xor_row(int x, int y) {
	range(i, 0, m - 1) a[x][i] ^= a[y][i];
}

// return rank
int gaussian(int x, int y) {
	if (x >= n) return n;
	if (y >= m) {
		return x;
	}
	int p = n;
	range(i, x, n - 1) if (a[i][y] == 1) { p = i; break; }
	if (p >= n) {
		return gaussian(x, y + 1);
	} else {
		if (x != p) swap_row(x, p);
		range(i, x + 1, n - 1) {
			if (a[i][y] == 0) continue;
			xor_row(i, x);
		}
		return gaussian(x + 1, y + 1);
	}
}

i64 qpow(i64 a, i64 b) {
	if (b == 0) return 1;
	i64 t = qpow(a, b >> 1ll);
	t = t * t % modp;
	if (b & 1) t = t * a % modp;
	return t;
}

int main() {
	cin >> n >> m;
	range(i, 0, n - 1) range(j, 0, m - 1) scanf("%d", &a[i][j]);
	int r = gaussian(0, 0);
	i64 ans = qpow(2, m - 1) * ((qpow(2, n) - qpow(2, n - r)) % modp) % modp;
	ans = (ans + modp) % modp;
	cout << ans << endl;
    return 0;
}
```