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

typedef long long ll;

const int Maxn = 305;
const int mod = 998244353;

int pw2[Maxn];
int n, m;
int M[Maxn][Maxn];

void Swap(int r1, int r2)
{
    for (int j = 0; j < m; j++)
        swap(M[r1][j], M[r2][j]);
}

void Add(int r1, int r2)
{
    for (int j = 0; j < m; j++)
        M[r2][j] ^= M[r1][j];
}

int main()
{
    pw2[0] = 1;
    for (int i = 1; i < Maxn; i++)
        pw2[i] = 2ll * pw2[i - 1] % mod;
    scanf("%d %d", &n, &m);
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++)
            scanf("%d", &M[i][j]);
    int r = 0;
    for (int j = 0; j < m; j++) {
        int i = r;
        while (i < n && M[i][j] == 0) i++;
        if (i == n) continue;
        Swap(i, r);
        for (int l = r + 1; l < n; l++) if (M[l][j])
            Add(r, l);
        r++;
    }
    int res = (pw2[n] - pw2[n - r] + mod) % mod;
    res = ll(res) * pw2[m - 1] % mod;
    printf("%d\n", res);
    return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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 Maxn = 305;
const int mod = 998244353;

int pw2[Maxn];
int n, m;
int M[Maxn][Maxn];

void Swap(int r1, int r2)
{
    for (int j = 0; j < m; j++)
        swap(M[r1][j], M[r2][j]);
}

void Add(int r1, int r2)
{
    for (int j = 0; j < m; j++)
        M[r2][j] ^= M[r1][j];
}

int main()
{
    pw2[0] = 1;
    for (int i = 1; i < Maxn; i++)
        pw2[i] = 2ll * pw2[i - 1] % mod;
    scanf("%d %d", &n, &m);
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++)
            scanf("%d", &M[i][j]);
    int r = 0;
    for (int j = 0; j < m; j++) {
        int i = r;
        while (i < n && M[i][j] == 0) i++;
        if (i == n) continue;
        Swap(i, r);
        for (int l = r + 1; l < n; l++) if (M[l][j])
            Add(r, l);
        r++;
    }
    int res = (pw2[n] - pw2[n - r] + mod) % mod;
    res = ll(res) * pw2[m - 1] % mod;
    printf("%d\n", res);
    return 0;
}

```