#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <cmath>
#include <map>
#include <queue>
#include <iomanip>
#include <set>
#define MOD 998244353
typedef long long ll;
using namespace std;

int N,M;
int A[303][303];

int Gauss(){
    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++;
        }
    }
    return rank;
}

ll my_pow(ll x,ll n){
    ll res=1;
    while(n>0){
        if(n&1) res=res*x%MOD;
        x=x*x%MOD;
        n/=2;
    }
    return res;
}

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

  int rank=Gauss();

  ll ans=my_pow(2ll,N-1+M)-my_pow(2ll,N-1+M-rank);
  ans=(ans+MOD)%MOD;

  cout<<ans<<endl;

  return 0;
}

### Prompt

Create a solution in cpp for 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 <cmath>
#include <map>
#include <queue>
#include <iomanip>
#include <set>
#define MOD 998244353
typedef long long ll;
using namespace std;

int N,M;
int A[303][303];

int Gauss(){
    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++;
        }
    }
    return rank;
}

ll my_pow(ll x,ll n){
    ll res=1;
    while(n>0){
        if(n&1) res=res*x%MOD;
        x=x*x%MOD;
        n/=2;
    }
    return res;
}

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

  int rank=Gauss();

  ll ans=my_pow(2ll,N-1+M)-my_pow(2ll,N-1+M-rank);
  ans=(ans+MOD)%MOD;

  cout<<ans<<endl;

  return 0;
}

```