#include <bits/stdc++.h>
using namespace std;

#define MOD 998244353

vector< vector<int> > A;

long long power(long long N, long long expo)
{
    long long ans = 1;
    
    while(expo)
    {
        if(expo % 2)
            ans = ans * N % MOD;
        
        N = N * N % MOD;
        expo /= 2;
    }
    
    return ans;
}

int main()
{
    ios::sync_with_stdio(0);
    cin.tie(NULL), cout.tie(NULL);

    int N, M;
    cin >> N >> M;
    
    for(int i=0; i<N; i++)
    {
        vector<int> B(M, 0);
        A.push_back(B);
        
        for(int j=0; j<M; j++)
        {
            int x;
            cin >> x;
            
            A[i][j] = x;
        }
    }
    
    long long ans = power(2, N) + MOD - 1;
    
    for(int i=0; i<N; i++)
    {
        int f = -1;
        sort(A.begin()+i, A.end(), greater< vector<int> >());
        
        for(int j=0; j<M; j++)
        {
            if(A[i][j] == 1)
            {
                f = j;
                break;
            }
        }
        
        if(f == -1)
        {
            ans += MOD - power(2, N-i) + 1;
            break;
        }
        
        for(int j=i+1; j<N; j++)
        {
            if(A[j][f] == 1)
            {
                for(int k=f; k<M; k++)
                    A[j][k] ^= A[i][k];
            }
        }
    }
    
    cout << ans % MOD * power(2, M-1) % MOD << "\n";
    return 0;
}
### Prompt

Please provide a CPP coded solution to the problem described below:

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 MOD 998244353

vector< vector<int> > A;

long long power(long long N, long long expo)
{
    long long ans = 1;
    
    while(expo)
    {
        if(expo % 2)
            ans = ans * N % MOD;
        
        N = N * N % MOD;
        expo /= 2;
    }
    
    return ans;
}

int main()
{
    ios::sync_with_stdio(0);
    cin.tie(NULL), cout.tie(NULL);

    int N, M;
    cin >> N >> M;
    
    for(int i=0; i<N; i++)
    {
        vector<int> B(M, 0);
        A.push_back(B);
        
        for(int j=0; j<M; j++)
        {
            int x;
            cin >> x;
            
            A[i][j] = x;
        }
    }
    
    long long ans = power(2, N) + MOD - 1;
    
    for(int i=0; i<N; i++)
    {
        int f = -1;
        sort(A.begin()+i, A.end(), greater< vector<int> >());
        
        for(int j=0; j<M; j++)
        {
            if(A[i][j] == 1)
            {
                f = j;
                break;
            }
        }
        
        if(f == -1)
        {
            ans += MOD - power(2, N-i) + 1;
            break;
        }
        
        for(int j=i+1; j<N; j++)
        {
            if(A[j][f] == 1)
            {
                for(int k=f; k<M; k++)
                    A[j][k] ^= A[i][k];
            }
        }
    }
    
    cout << ans % MOD * power(2, M-1) % MOD << "\n";
    return 0;
}
```