#include <iostream>
#include <algorithm>
typedef long long ll;
using namespace std;

int a[310][310];
ll mod=998244353, beki[310];

int main(void){
    int N, M;
    cin >> N >> M;
    for(int i=0; i<N; ++i){
        for(int j=0; j<M; ++j){
            cin >> a[i][j];
        }
    }
    beki[0]=1;
    for(int i=1; i<310; ++i){
        beki[i]=(beki[i-1]*2)%mod;
    }
    int cnt=0;
    for(int i=0; i<N; ++i){
        int piv=cnt;
        while(piv<M){
            if(a[i][piv]==1) break;
            ++piv;
        }
        if(piv<M){
            for(int j=0; j<N; ++j){
                swap(a[j][cnt], a[j][piv]);
            }
            for(int j=cnt+1; j<M; ++j){
                if(a[i][j]==1){
                    for(int k=0; k<N; ++k){
                        a[k][j] ^= a[k][cnt];
                    }
                }
            }
            ++cnt;
        }
    }
    ll ans=(beki[M]+mod-beki[M-cnt])%mod;
    (ans *= beki[N-1]) %= mod;
    cout << ans << endl;
    return 0;
}

### Prompt

Your task is to create a Cpp solution 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>
typedef long long ll;
using namespace std;

int a[310][310];
ll mod=998244353, beki[310];

int main(void){
    int N, M;
    cin >> N >> M;
    for(int i=0; i<N; ++i){
        for(int j=0; j<M; ++j){
            cin >> a[i][j];
        }
    }
    beki[0]=1;
    for(int i=1; i<310; ++i){
        beki[i]=(beki[i-1]*2)%mod;
    }
    int cnt=0;
    for(int i=0; i<N; ++i){
        int piv=cnt;
        while(piv<M){
            if(a[i][piv]==1) break;
            ++piv;
        }
        if(piv<M){
            for(int j=0; j<N; ++j){
                swap(a[j][cnt], a[j][piv]);
            }
            for(int j=cnt+1; j<M; ++j){
                if(a[i][j]==1){
                    for(int k=0; k<N; ++k){
                        a[k][j] ^= a[k][cnt];
                    }
                }
            }
            ++cnt;
        }
    }
    ll ans=(beki[M]+mod-beki[M-cnt])%mod;
    (ans *= beki[N-1]) %= mod;
    cout << ans << endl;
    return 0;
}

```