#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
#include <queue>
#include <cstdio>
#include <complex>
#include <numeric>
#include <string.h>
#include <random>
#define rep(i,n) for (int i = 0; i < (int)n; i++)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pi;
typedef pair<pi, pi> pp;
typedef pair<ll, ll> pl;
double PI = 3.141592653589793238462643383279;
const double EPS = 1e-9;
const ll MOD = 998244353;
const int inf = 1 << 30;
const ll linf = 1LL << 60;

int calc_rank(vector<vector<int>> v) {
    int n = v.size(), m = v[0].size();
    int st = 0;
    rep(j,m) {
        int pv = -1;
        for (int i = st; i < n; i++) {
            if (v[i][j]) {
                pv = i;
                break;
            }
        }
        if (pv == -1) continue;
        if (pv != st) {
            swap(v[st], v[pv]);
        }
        for (int i = st+1; i < n; i++) {
            if (!v[i][j]) continue;
            for (int k = j; k < m; k++) {
                v[i][k] ^= v[st][k];
            }
        }
        st++;
    }
    return st;
}

int n, m;

int main() {
    cin >> n >> m;
    vector<vector<int>> a(n, vector<int>(m, 0));
    rep(i,n) rep(j,m) cin >> a[i][j];
    int r = calc_rank(a);
    ll ans = 1;
    rep(i,n+m-1) ans = ans * 2 % MOD;
    ll tmp = 1;
    rep(i,n+m-r-1) tmp = tmp * 2 % MOD;
    cout << (ans-tmp+MOD) % MOD << endl;
}
### Prompt

Please create a solution in Cpp 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 <algorithm>
#include <string>
#include <vector>
#include <map>
#include <queue>
#include <cstdio>
#include <complex>
#include <numeric>
#include <string.h>
#include <random>
#define rep(i,n) for (int i = 0; i < (int)n; i++)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pi;
typedef pair<pi, pi> pp;
typedef pair<ll, ll> pl;
double PI = 3.141592653589793238462643383279;
const double EPS = 1e-9;
const ll MOD = 998244353;
const int inf = 1 << 30;
const ll linf = 1LL << 60;

int calc_rank(vector<vector<int>> v) {
    int n = v.size(), m = v[0].size();
    int st = 0;
    rep(j,m) {
        int pv = -1;
        for (int i = st; i < n; i++) {
            if (v[i][j]) {
                pv = i;
                break;
            }
        }
        if (pv == -1) continue;
        if (pv != st) {
            swap(v[st], v[pv]);
        }
        for (int i = st+1; i < n; i++) {
            if (!v[i][j]) continue;
            for (int k = j; k < m; k++) {
                v[i][k] ^= v[st][k];
            }
        }
        st++;
    }
    return st;
}

int n, m;

int main() {
    cin >> n >> m;
    vector<vector<int>> a(n, vector<int>(m, 0));
    rep(i,n) rep(j,m) cin >> a[i][j];
    int r = calc_rank(a);
    ll ans = 1;
    rep(i,n+m-1) ans = ans * 2 % MOD;
    ll tmp = 1;
    rep(i,n+m-r-1) tmp = tmp * 2 % MOD;
    cout << (ans-tmp+MOD) % MOD << endl;
}
```