#include<bits/stdc++.h>

#define fec(i, x, y) (int i = head[x], y = g[i].to; i; i = g[i].ne, y = g[i].to)
#define dbg(...) fprintf(stderr, __VA_ARGS__)
#define File(x) freopen(#x".in", "r", stdin), freopen(#x".out", "w", stdout)
#define fi first
#define se second
#define pb push_back

template<typename A, typename B> inline char SMAX(A &a, const B &b) {return a < b ? a = b , 1 : 0;}
template<typename A, typename B> inline char SMIN(A &a, const B &b) {return b < a ? a = b , 1 : 0;}

typedef long long ll; typedef unsigned long long ull; typedef std::pair<int, int> pii;

template<typename I>
inline void read(I &x) {
	int f = 0, c;
	while (!isdigit(c = getchar())) c == '-' ? f = 1 : 0;
	x = c & 15;
	while (isdigit(c = getchar())) x = (x << 1) + (x << 3) + (c & 15);
	f ? x = -x : 0;
}

const int N = 300 + 7;
const int P = 998244353;

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

inline int fpow(int x, int y) {
	int ans = 1;
	for (; y; y >>= 1, x = (ll)x * x % P) if (y & 1) ans = (ll)ans * x % P;
	return ans;
}

int main() {
	#ifdef hzhkk
	freopen("hkk.in", "r", stdin);
	#endif
	read(n), read(m);
	for (int i = 1; i <= n; ++i) for (int j = 1; j <= m; ++j) read(a[i][j]);
	for (int i = 1; i <= n; ++i){
		for (int j = 1; j <= m; ++j)
			if (a[i][j])
				if (!b[j][j]) {
					for (int k = 1; k <= m; ++k) b[j][k] = a[i][k];
					++r;
					break;
				} else for (int k = 1; k <= m; ++k) a[i][k] ^= b[j][k];
	}
	printf("%lld\n", (ll)fpow(2, m - 1) * (fpow(2, n) + P - fpow(2, n - r)) % P);
}
### Prompt

Create a solution in CPP for 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 fec(i, x, y) (int i = head[x], y = g[i].to; i; i = g[i].ne, y = g[i].to)
#define dbg(...) fprintf(stderr, __VA_ARGS__)
#define File(x) freopen(#x".in", "r", stdin), freopen(#x".out", "w", stdout)
#define fi first
#define se second
#define pb push_back

template<typename A, typename B> inline char SMAX(A &a, const B &b) {return a < b ? a = b , 1 : 0;}
template<typename A, typename B> inline char SMIN(A &a, const B &b) {return b < a ? a = b , 1 : 0;}

typedef long long ll; typedef unsigned long long ull; typedef std::pair<int, int> pii;

template<typename I>
inline void read(I &x) {
	int f = 0, c;
	while (!isdigit(c = getchar())) c == '-' ? f = 1 : 0;
	x = c & 15;
	while (isdigit(c = getchar())) x = (x << 1) + (x << 3) + (c & 15);
	f ? x = -x : 0;
}

const int N = 300 + 7;
const int P = 998244353;

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

inline int fpow(int x, int y) {
	int ans = 1;
	for (; y; y >>= 1, x = (ll)x * x % P) if (y & 1) ans = (ll)ans * x % P;
	return ans;
}

int main() {
	#ifdef hzhkk
	freopen("hkk.in", "r", stdin);
	#endif
	read(n), read(m);
	for (int i = 1; i <= n; ++i) for (int j = 1; j <= m; ++j) read(a[i][j]);
	for (int i = 1; i <= n; ++i){
		for (int j = 1; j <= m; ++j)
			if (a[i][j])
				if (!b[j][j]) {
					for (int k = 1; k <= m; ++k) b[j][k] = a[i][k];
					++r;
					break;
				} else for (int k = 1; k <= m; ++k) a[i][k] ^= b[j][k];
	}
	printf("%lld\n", (ll)fpow(2, m - 1) * (fpow(2, n) + P - fpow(2, n - r)) % P);
}
```