#include<bits/stdc++.h>
using namespace std;

typedef long long ll;
ll const mod = 998244353;

#define p_ary(ary,a,b,i) do { cout << "["; for (int (i) = (a);(i) < (b);++(i)) cout << ary[(i)] << ((b)-1 == (i) ? "" : ", "); cout << "]\n"; } while(0)
#define p_map(map,it) do {cout << "{";for (auto (it) = map.begin();;++(it)) {if ((it) == map.end()) {cout << "}\n";break;}else cout << "" << (it)->first << "=>" << (it)->second << ", ";}}while(0)

ll power_mod(ll a,ll b,ll mod) {
    if (b == 0) return 1;
    if (b == 1) return a;
    ll c = power_mod(a,b/2,mod);
    if (b%2) return c*c%mod*a%mod;
    else return c*c%mod;
}

int main() {
    int n,m;
    cin >> n >> m;
    bool a[n][m];
    int r = 0;
    for (int i = 0;i < n;++i) for (int j = 0;j < m;++j) cin >> a[i][j];
    for (int i = 0;i < min(n,m);++i) {
        int p = i,q = i;
        for (int j = i;j < n;++j) {
            if (a[p][q]) break;
            for (int k = i;k < m;++k) if (a[j][k]) {
                p = j;q = k;
                break;
            }
        }
        if (!a[p][q]) break;
        r = i+1;
        for (int j = i;j < n;++j) swap(a[j][i],a[j][q]);
        for (int j = i;j < m;++j) swap(a[i][j],a[p][j]);
        for (int j = i+1;j < n;++j) if (a[j][i]) for (int k = i;k < m;++k) a[j][k] ^= a[i][k];
        for (int j = i+1;j < m;++j) if (a[i][j]) for (int k = i;k < n;++k) a[k][j] ^= a[k][i];
    }
    cout << (power_mod(2,n+m-1,mod)-power_mod(2,n+m-r-1,mod)+mod)%mod << endl;
    return 0;
}
### 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<bits/stdc++.h>
using namespace std;

typedef long long ll;
ll const mod = 998244353;

#define p_ary(ary,a,b,i) do { cout << "["; for (int (i) = (a);(i) < (b);++(i)) cout << ary[(i)] << ((b)-1 == (i) ? "" : ", "); cout << "]\n"; } while(0)
#define p_map(map,it) do {cout << "{";for (auto (it) = map.begin();;++(it)) {if ((it) == map.end()) {cout << "}\n";break;}else cout << "" << (it)->first << "=>" << (it)->second << ", ";}}while(0)

ll power_mod(ll a,ll b,ll mod) {
    if (b == 0) return 1;
    if (b == 1) return a;
    ll c = power_mod(a,b/2,mod);
    if (b%2) return c*c%mod*a%mod;
    else return c*c%mod;
}

int main() {
    int n,m;
    cin >> n >> m;
    bool a[n][m];
    int r = 0;
    for (int i = 0;i < n;++i) for (int j = 0;j < m;++j) cin >> a[i][j];
    for (int i = 0;i < min(n,m);++i) {
        int p = i,q = i;
        for (int j = i;j < n;++j) {
            if (a[p][q]) break;
            for (int k = i;k < m;++k) if (a[j][k]) {
                p = j;q = k;
                break;
            }
        }
        if (!a[p][q]) break;
        r = i+1;
        for (int j = i;j < n;++j) swap(a[j][i],a[j][q]);
        for (int j = i;j < m;++j) swap(a[i][j],a[p][j]);
        for (int j = i+1;j < n;++j) if (a[j][i]) for (int k = i;k < m;++k) a[j][k] ^= a[i][k];
        for (int j = i+1;j < m;++j) if (a[i][j]) for (int k = i;k < n;++k) a[k][j] ^= a[k][i];
    }
    cout << (power_mod(2,n+m-1,mod)-power_mod(2,n+m-r-1,mod)+mod)%mod << endl;
    return 0;
}
```