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

const int64_t MOD = 998244353;

int64_t power_mod(int64_t num, int64_t power){
    int64_t prod = 1;
    num %= MOD;
    while(power > 0){
        if(power&1) prod = prod * num % MOD;
        num = num * num % MOD;
        power >>= 1;
    }
    return prod;
}

int main(){
    int N, M, A[300][300];
    cin >> N >> M;
    for(int i=0; i<N; i++) for(int j=0; j<M; j++) cin >> A[i][j];

    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 >= 0){
            if(pivot != rank) for(int k=0; k<M; k++) swap(A[pivot][k], A[rank][k]);
            for(int i=rank+1; i<N; i++){
                if(A[i][j]) for(int k=0; k<M; k++) A[i][k] ^= A[rank][k];
            }
            rank++;
        }
    }

    int64_t ans = (MOD + power_mod(2, N+M-1) - power_mod(2, N+M-rank-1)) % MOD;
    cout << ans << endl;
    return 0;
}
### Prompt

Develop a solution in Cpp to the problem described below:

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;

const int64_t MOD = 998244353;

int64_t power_mod(int64_t num, int64_t power){
    int64_t prod = 1;
    num %= MOD;
    while(power > 0){
        if(power&1) prod = prod * num % MOD;
        num = num * num % MOD;
        power >>= 1;
    }
    return prod;
}

int main(){
    int N, M, A[300][300];
    cin >> N >> M;
    for(int i=0; i<N; i++) for(int j=0; j<M; j++) cin >> A[i][j];

    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 >= 0){
            if(pivot != rank) for(int k=0; k<M; k++) swap(A[pivot][k], A[rank][k]);
            for(int i=rank+1; i<N; i++){
                if(A[i][j]) for(int k=0; k<M; k++) A[i][k] ^= A[rank][k];
            }
            rank++;
        }
    }

    int64_t ans = (MOD + power_mod(2, N+M-1) - power_mod(2, N+M-rank-1)) % MOD;
    cout << ans << endl;
    return 0;
}
```