#include<bits/stdc++.h>

#define ll long long
#define fornum(A,B,C) for(A=B;A<C;A++)
#define mp make_pair
#define pii pair<int,int>
#define pll pair<ll,ll>

using namespace std;

/////////////////////////////////////////////////////
#define MOD 998244353


ll N,M;
ll a[333][333];
ll dp1[333][333][2],dp2[333][333][2],dp3[333][333][2];
ll i,j,k,l,ans;
inline void addd(ll aa,ll bb){
    if(aa==bb)
        return;
    ll i;
    fornum(i,0,M){
        a[aa][i] = (a[aa][i] + a[bb][i]) % 2;
    }
}
int main(){
    scanf("%lld%lld", &N, &M);
    fornum(i,0,N){
        fornum(j,0,M){
            scanf("%lld", &a[i][j]);
        }
    }
    k = 0;
    fornum(i,0,M){
        fornum(j,k,N){
            if(a[j][i]){
                addd(k, j);
                break;
            }
        }
        //printf("%lld,%lld,%lld\n", i, j, k);
        if(j==N)
            continue;
        fornum(j,k+1,N){
            if(a[j][i]){
                addd(j, k);
            }
        }
        k++;
        
    }
    j = 1;
    fornum(i,1,N+M-k){
        j = (j * 2) % MOD;
    }
    //printf("%lld\n", j);
    ans = 1;
    fornum(i,1,N+M){
        ans = (ans * 2) % MOD;
    }
    //printf("%lld\n", ans);
    ans = (ans + MOD - j) % MOD;

    printf("%lld\n", ans);
    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>

#define ll long long
#define fornum(A,B,C) for(A=B;A<C;A++)
#define mp make_pair
#define pii pair<int,int>
#define pll pair<ll,ll>

using namespace std;

/////////////////////////////////////////////////////
#define MOD 998244353


ll N,M;
ll a[333][333];
ll dp1[333][333][2],dp2[333][333][2],dp3[333][333][2];
ll i,j,k,l,ans;
inline void addd(ll aa,ll bb){
    if(aa==bb)
        return;
    ll i;
    fornum(i,0,M){
        a[aa][i] = (a[aa][i] + a[bb][i]) % 2;
    }
}
int main(){
    scanf("%lld%lld", &N, &M);
    fornum(i,0,N){
        fornum(j,0,M){
            scanf("%lld", &a[i][j]);
        }
    }
    k = 0;
    fornum(i,0,M){
        fornum(j,k,N){
            if(a[j][i]){
                addd(k, j);
                break;
            }
        }
        //printf("%lld,%lld,%lld\n", i, j, k);
        if(j==N)
            continue;
        fornum(j,k+1,N){
            if(a[j][i]){
                addd(j, k);
            }
        }
        k++;
        
    }
    j = 1;
    fornum(i,1,N+M-k){
        j = (j * 2) % MOD;
    }
    //printf("%lld\n", j);
    ans = 1;
    fornum(i,1,N+M){
        ans = (ans * 2) % MOD;
    }
    //printf("%lld\n", ans);
    ans = (ans + MOD - j) % MOD;

    printf("%lld\n", ans);
    return 0;
}
```