#include <bits/stdc++.h>

using namespace std;

#define LL long long
#define _rep(i,j,N) for(int i = (j);i <=(N);i++)
#define _for(i,j,N) for(int i = (j);i <(N);i++)
#define ALL(x) x.begin(),x.end()

const int mod = 998244353;
const int maxn = 305;
int N,M;
string G[maxn];

void xors(string &a,string &b){
    _for(i,0,M){
        if(a[i] == b[i]) b[i] = '0';
        else b[i] = '1';
    }
}

int pow_mod(int a,int n,int m){
    if(n == 0) return 1;
    int x = pow_mod(a,n/2,m);
    LL ans = ((LL)x * x) % m;
    if(n & 1) ans = ans * a % m;
    return (int) ans;

}

int main()
{
    cin >> N >> M;
    _for(i,0,N){
        _for(j,0,M){
            string s;
            cin >> s;
            G[i].push_back(s[0]);
        }
    }

    int r = -1;
    _for(i,0,N){
        sort(G+i,G+N,greater<string>());
        int index = -1;
        _for(j,0,M) if(G[i][j] == '1'){index = j;break;}
        if(index == -1){r = i;break;}
        _for(j,i+1,N){
            if(G[j][index] == '1'){
                xors(G[i],G[j]);
            }
        }
    }
    if(r == -1) r = N;
    int a = pow_mod(2,M+N-1,mod);
    int b = pow_mod(2,M+N-r-1,mod);
    int ans = ((LL)a - b + mod)%mod;
    printf("%d\n",ans);
    return 0;
}

### Prompt

Your challenge is to write 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 LL long long
#define _rep(i,j,N) for(int i = (j);i <=(N);i++)
#define _for(i,j,N) for(int i = (j);i <(N);i++)
#define ALL(x) x.begin(),x.end()

const int mod = 998244353;
const int maxn = 305;
int N,M;
string G[maxn];

void xors(string &a,string &b){
    _for(i,0,M){
        if(a[i] == b[i]) b[i] = '0';
        else b[i] = '1';
    }
}

int pow_mod(int a,int n,int m){
    if(n == 0) return 1;
    int x = pow_mod(a,n/2,m);
    LL ans = ((LL)x * x) % m;
    if(n & 1) ans = ans * a % m;
    return (int) ans;

}

int main()
{
    cin >> N >> M;
    _for(i,0,N){
        _for(j,0,M){
            string s;
            cin >> s;
            G[i].push_back(s[0]);
        }
    }

    int r = -1;
    _for(i,0,N){
        sort(G+i,G+N,greater<string>());
        int index = -1;
        _for(j,0,M) if(G[i][j] == '1'){index = j;break;}
        if(index == -1){r = i;break;}
        _for(j,i+1,N){
            if(G[j][index] == '1'){
                xors(G[i],G[j]);
            }
        }
    }
    if(r == -1) r = N;
    int a = pow_mod(2,M+N-1,mod);
    int b = pow_mod(2,M+N-r-1,mod);
    int ans = ((LL)a - b + mod)%mod;
    printf("%d\n",ans);
    return 0;
}

```