        #include <bits/stdc++.h>
        using namespace std;
   #define int long long
    const int MAX =200002;
const int MOD =  998244353;
int modpow(int a, int n, int mod) {
    int res = 1;
    while (n > 0) {
        if (n & 1) res = res * a % mod;
        a = a * a % mod;
        n >>= 1;
    }
    return res;
}
     signed main(){
  int n,m,k;
  cin>>n>>m;
  bitset<300> a[n];
  for(int i=0;i<n;i++)for(int j=0;j<m;j++){
      cin>>k;
      if(k)a[i].set(j);
      else a[i].reset(j);
  }
  int j0=0;
  for(int i=0;i<m;i++){
      for(int j=j0;j<n;j++){
          if(a[j][i]){
              swap(a[j],a[j0]);
              break;
          }
      }
      if(a[j0][i]){
          for(int j=j0+1;j<n;j++){
              if(a[j][i])a[j]^=a[j0];
          }
          j0++;
      }
  }

  cout<<(MOD+modpow(2,n,MOD)-modpow(2,n-j0,MOD))%MOD*modpow(2,m-1,MOD)%MOD<<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;
   #define int long long
    const int MAX =200002;
const int MOD =  998244353;
int modpow(int a, int n, int mod) {
    int res = 1;
    while (n > 0) {
        if (n & 1) res = res * a % mod;
        a = a * a % mod;
        n >>= 1;
    }
    return res;
}
     signed main(){
  int n,m,k;
  cin>>n>>m;
  bitset<300> a[n];
  for(int i=0;i<n;i++)for(int j=0;j<m;j++){
      cin>>k;
      if(k)a[i].set(j);
      else a[i].reset(j);
  }
  int j0=0;
  for(int i=0;i<m;i++){
      for(int j=j0;j<n;j++){
          if(a[j][i]){
              swap(a[j],a[j0]);
              break;
          }
      }
      if(a[j0][i]){
          for(int j=j0+1;j<n;j++){
              if(a[j][i])a[j]^=a[j0];
          }
          j0++;
      }
  }

  cout<<(MOD+modpow(2,n,MOD)-modpow(2,n-j0,MOD))%MOD*modpow(2,m-1,MOD)%MOD<<endl;



     }


 


 






    





      

        

```