#include <iostream>
#include <vector>
#include <map>
#include <algorithm>
#include <queue>
using namespace std;

int N, M;
int mod = 998244353;

int power(int a, int n){
    if (n == 0) {
        return 1;
    } else if (n % 2 == 0) {
        int b = power(a, n / 2);
        return 1ll * b * b % mod;
    } else {
        return 1ll * a * power(a, n - 1) % mod;
    }
}

int main() {
    cin >> N >> M;
    vector<vector<int>> A(N, vector<int>(M));
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < M; j++) {
            cin >> A[i][j];
        }
    }
    
//    rank計算
    int rank = 0;
    for (int j = 0; j < M; j++) {
        int pivot = -1;
        for (int i = rank; i < N; i++) {
            if (A[i][j]) {
                pivot = i;
                break;
            }
        }
        if (pivot != -1) {
            swap(A[rank], A[pivot]);
            for (int i = rank + 1; i < N; i++) {
                if (A[i][j]) {
                    for (int k = j; k < M; k++) {
                        A[i][k] ^= A[rank][k];
                    }
                }
            }
            rank++;
        }
    }
    int a = power(2, N + M - 1), b = power(2, N + M - rank - 1);
    cout << (a - b + mod) % mod << endl;
}
### 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 <iostream>
#include <vector>
#include <map>
#include <algorithm>
#include <queue>
using namespace std;

int N, M;
int mod = 998244353;

int power(int a, int n){
    if (n == 0) {
        return 1;
    } else if (n % 2 == 0) {
        int b = power(a, n / 2);
        return 1ll * b * b % mod;
    } else {
        return 1ll * a * power(a, n - 1) % mod;
    }
}

int main() {
    cin >> N >> M;
    vector<vector<int>> A(N, vector<int>(M));
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < M; j++) {
            cin >> A[i][j];
        }
    }
    
//    rank計算
    int rank = 0;
    for (int j = 0; j < M; j++) {
        int pivot = -1;
        for (int i = rank; i < N; i++) {
            if (A[i][j]) {
                pivot = i;
                break;
            }
        }
        if (pivot != -1) {
            swap(A[rank], A[pivot]);
            for (int i = rank + 1; i < N; i++) {
                if (A[i][j]) {
                    for (int k = j; k < M; k++) {
                        A[i][k] ^= A[rank][k];
                    }
                }
            }
            rank++;
        }
    }
    int a = power(2, N + M - 1), b = power(2, N + M - rank - 1);
    cout << (a - b + mod) % mod << endl;
}
```