#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=305,mod=998244353;
int n,m,a[N][N],b[N][N];
ll qpow(ll a,ll n)
{
    ll ans=1;
    while(n)
    {
        if(n&1) ans=ans*a%mod;
        a=a*a%mod;
        n>>=1;
    }
    return ans;
}
int guass(int n)
{
    int ans=0;
    for(int i=1;i<=n;i++)
    {
        int p=i;
        while(p<=n&&!a[i][p]) p++;
        if(p==n+1) {ans++;continue;}
        swap(a[i],a[p]);
        for(int j=i+1;j<=n;j++)
            if(a[j][i])
            for(int k=i;k<=n;k++)
            a[j][k]^=a[i][k];
    }
    return ans;
}
int main()
{
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++)
        for(int j=1;j<=m;j++)
        scanf("%d",&a[i][j]);
    int r=0;
    for(int i=1;i<=n;i++)
        for(int j=1;j<=m;j++)
        if(a[i][j])
        {
            if(b[j][j]) for(int k=j;k<=m;k++) a[i][k]^=b[j][k];
            else
            {
                for(int k=j;k<=m;k++) b[j][k]=a[i][k];
                r++;break;
            }
        }
    printf("%lld\n",qpow(2,n-1)*(qpow(2,m)+mod-qpow(2,m-r))%mod);
}

### Prompt

Develop a solution in cpp 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;
typedef long long ll;
const int N=305,mod=998244353;
int n,m,a[N][N],b[N][N];
ll qpow(ll a,ll n)
{
    ll ans=1;
    while(n)
    {
        if(n&1) ans=ans*a%mod;
        a=a*a%mod;
        n>>=1;
    }
    return ans;
}
int guass(int n)
{
    int ans=0;
    for(int i=1;i<=n;i++)
    {
        int p=i;
        while(p<=n&&!a[i][p]) p++;
        if(p==n+1) {ans++;continue;}
        swap(a[i],a[p]);
        for(int j=i+1;j<=n;j++)
            if(a[j][i])
            for(int k=i;k<=n;k++)
            a[j][k]^=a[i][k];
    }
    return ans;
}
int main()
{
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++)
        for(int j=1;j<=m;j++)
        scanf("%d",&a[i][j]);
    int r=0;
    for(int i=1;i<=n;i++)
        for(int j=1;j<=m;j++)
        if(a[i][j])
        {
            if(b[j][j]) for(int k=j;k<=m;k++) a[i][k]^=b[j][k];
            else
            {
                for(int k=j;k<=m;k++) b[j][k]=a[i][k];
                r++;break;
            }
        }
    printf("%lld\n",qpow(2,n-1)*(qpow(2,m)+mod-qpow(2,m-r))%mod);
}

```