# include <bits/stdc++.h>
using namespace std;
typedef long long ll;
     
const int maxn(305);
const int mod(998244353);

inline void Inc(int &x, int y) {
    x = x + y >= mod ? x + y - mod : x + y;
}

inline void Dec(int &x, int y) {
    x = x - y < 0 ? x - y + mod : x - y;
}

inline int Add(int x, int y) {
    return x + y >= mod ? x + y - mod : x + y;
}

inline int Sub(int x, int y) {
    return x - y < 0 ? x - y + mod : x - y;
}

inline int Pow(ll x, int y) {
    ll ret = 1;
    for (; y; y >>= 1, x = x * x % mod)
        if (y & 1) ret = ret * x % mod;
    return ret;
}

int n, m, ans, cnt, tot;
bitset <maxn> a, b[maxn];

inline void Insert() {
	int i;
	if (tot == m) return;
	for (i = 1; i <= m; ++i)
		if (a[i]) {
			if (!b[i][i]) {
				b[i] = a, ++tot;
				return;
			}
			a ^= b[i];
		}
	return;
}

int main() {
	int i, j, v;
	scanf("%d%d", &n, &m);
	for (i = 1; i <= n; ++i) {
		a.reset();
		for (j = 1; j <= m; ++j) {
			scanf("%d", &v);
			if (v) a.set(j);
		}
		Insert();
	}
	ans = Pow(2, n), Dec(ans, Pow(2, n - tot));
	ans = (ll)ans * Pow(2, m - 1) % mod;
	printf("%d\n", ans);
	return 0;
}
### Prompt

Construct a cpp code solution to the problem outlined:

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 int maxn(305);
const int mod(998244353);

inline void Inc(int &x, int y) {
    x = x + y >= mod ? x + y - mod : x + y;
}

inline void Dec(int &x, int y) {
    x = x - y < 0 ? x - y + mod : x - y;
}

inline int Add(int x, int y) {
    return x + y >= mod ? x + y - mod : x + y;
}

inline int Sub(int x, int y) {
    return x - y < 0 ? x - y + mod : x - y;
}

inline int Pow(ll x, int y) {
    ll ret = 1;
    for (; y; y >>= 1, x = x * x % mod)
        if (y & 1) ret = ret * x % mod;
    return ret;
}

int n, m, ans, cnt, tot;
bitset <maxn> a, b[maxn];

inline void Insert() {
	int i;
	if (tot == m) return;
	for (i = 1; i <= m; ++i)
		if (a[i]) {
			if (!b[i][i]) {
				b[i] = a, ++tot;
				return;
			}
			a ^= b[i];
		}
	return;
}

int main() {
	int i, j, v;
	scanf("%d%d", &n, &m);
	for (i = 1; i <= n; ++i) {
		a.reset();
		for (j = 1; j <= m; ++j) {
			scanf("%d", &v);
			if (v) a.set(j);
		}
		Insert();
	}
	ans = Pow(2, n), Dec(ans, Pow(2, n - tot));
	ans = (ll)ans * Pow(2, m - 1) % mod;
	printf("%d\n", ans);
	return 0;
}
```