#define _CRT_SECURE_NO_WARNINGS
#include<bits/stdc++.h>
using namespace std;
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define LL long long
#define pb push_back

const int N = 305;
const int MOD = 998244353;
bitset<N> a[N];
vector<bitset<N>> base;
LL q_pow(LL n, LL k) {
	LL res = 1;
	while (k) {
		if (k & 1) res = (res*n) % MOD;
		k >>= 1;
		n = (n*n) % MOD;
	}
	return res;
}
int main() {
	int n, m, t;
	scanf("%d %d", &n, &m);
	for (int i = 0; i < n; ++i) {
		a[i].reset();
		for (int j = m - 1; j >= 0; --j) {
			scanf("%d", &t);
			if (t) a[i].flip(j);
		}
	}
	for (int i = 0; i < n; i++) {
		for (bitset<N> b : base) {
			bitset<N> bb = b ^ a[i];
			for (int j = 0; j < m; j++) {
				if (bb[j] < a[i][j]) {
					a[i] = bb;
					break;
				}
				else if (bb[j] > a[i][j]) break;
			}
		}
		if (a[i].any()) base.pb(a[i]);
	}
	int cnt = (int)base.size();
	printf("%lld\n", ((q_pow(2, n + m - 1) - q_pow(2, n + m - 1 - cnt)) % MOD + MOD) % MOD);
	//system("pause");
	return 0;
}

### Prompt

In cpp, your task is to solve 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
#define _CRT_SECURE_NO_WARNINGS
#include<bits/stdc++.h>
using namespace std;
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define LL long long
#define pb push_back

const int N = 305;
const int MOD = 998244353;
bitset<N> a[N];
vector<bitset<N>> base;
LL q_pow(LL n, LL k) {
	LL res = 1;
	while (k) {
		if (k & 1) res = (res*n) % MOD;
		k >>= 1;
		n = (n*n) % MOD;
	}
	return res;
}
int main() {
	int n, m, t;
	scanf("%d %d", &n, &m);
	for (int i = 0; i < n; ++i) {
		a[i].reset();
		for (int j = m - 1; j >= 0; --j) {
			scanf("%d", &t);
			if (t) a[i].flip(j);
		}
	}
	for (int i = 0; i < n; i++) {
		for (bitset<N> b : base) {
			bitset<N> bb = b ^ a[i];
			for (int j = 0; j < m; j++) {
				if (bb[j] < a[i][j]) {
					a[i] = bb;
					break;
				}
				else if (bb[j] > a[i][j]) break;
			}
		}
		if (a[i].any()) base.pb(a[i]);
	}
	int cnt = (int)base.size();
	printf("%lld\n", ((q_pow(2, n + m - 1) - q_pow(2, n + m - 1 - cnt)) % MOD + MOD) % MOD);
	//system("pause");
	return 0;
}

```