#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define fr(i,n) for(int i=0;i<n;i++)
#define Fr(i,n) for(int i=0;i++<n;)
#define ifr(i,n) for(int i=n-1;i>=0;i--)

const ll MOD=998244353;
ll n,m,a[310][310];

ll ad(ll x,ll y){
  return (x+y)%MOD;
}

ll mlt(ll x,ll y){
  return (x*y)%MOD;
}

ll pwr(ll x,ll y){
  ll pw[32]={},w=1;
  pw[0]=x;
  fr(i,31) pw[i+1]=mlt(pw[i],pw[i]);
  fr(i,32){
    w=mlt(w,1+(y%2)*(pw[i]-1));
    y/=2;
  }
  return w;
}

ll rnk(ll n,ll m,ll M[][310]){
  ll t=0,y=0;
  bool f;
  for(;;){
    f=0;
    if(M[t][y]==0){
      f=1;
      for(ll i=t+1;i<n;i++){
        if(M[i][y]!=0){
          f=0;
          swap(M[t],M[i]);
        }
      }
    }
    if(f && y<m-1){y++;continue;}
    if(f) return t;
    for(ll i=t+1;i<n;i++){
      if(M[i][y]==0) continue;
      for(ll j=y;j<m;j++){
        M[i][j]=(M[i][j]+M[t][j])%2;
      }
    }
    t++;
    if(t==n) return n;
  }
}

int main(){
  cin>>n>>m;
  fr(i,n) fr(j,m) cin>>a[i][j];
  cout<<ad(pwr(2,n+m-1),MOD-pwr(2,n+m-1-rnk(n,m,a)))<<endl;
}
### Prompt

Please formulate 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<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define fr(i,n) for(int i=0;i<n;i++)
#define Fr(i,n) for(int i=0;i++<n;)
#define ifr(i,n) for(int i=n-1;i>=0;i--)

const ll MOD=998244353;
ll n,m,a[310][310];

ll ad(ll x,ll y){
  return (x+y)%MOD;
}

ll mlt(ll x,ll y){
  return (x*y)%MOD;
}

ll pwr(ll x,ll y){
  ll pw[32]={},w=1;
  pw[0]=x;
  fr(i,31) pw[i+1]=mlt(pw[i],pw[i]);
  fr(i,32){
    w=mlt(w,1+(y%2)*(pw[i]-1));
    y/=2;
  }
  return w;
}

ll rnk(ll n,ll m,ll M[][310]){
  ll t=0,y=0;
  bool f;
  for(;;){
    f=0;
    if(M[t][y]==0){
      f=1;
      for(ll i=t+1;i<n;i++){
        if(M[i][y]!=0){
          f=0;
          swap(M[t],M[i]);
        }
      }
    }
    if(f && y<m-1){y++;continue;}
    if(f) return t;
    for(ll i=t+1;i<n;i++){
      if(M[i][y]==0) continue;
      for(ll j=y;j<m;j++){
        M[i][j]=(M[i][j]+M[t][j])%2;
      }
    }
    t++;
    if(t==n) return n;
  }
}

int main(){
  cin>>n>>m;
  fr(i,n) fr(j,m) cin>>a[i][j];
  cout<<ad(pwr(2,n+m-1),MOD-pwr(2,n+m-1-rnk(n,m,a)))<<endl;
}
```