#include <bits/stdc++.h>

const int MAXN = 310;
const int mod = 998244353;

int n, m;
std::bitset<MAXN> bs[MAXN];
int pow2[MAXN];

int main() {
    pow2[0] = 1;
    for (int i = 1; i < MAXN; ++i) {
        pow2[i] = 2 * pow2[i - 1] % mod;
    }
    scanf("%d%d", &n, &m);
    for (int i = 0; i < n; ++i) {
        for (int j = 0, x; j < m; ++j) {
            scanf("%d", &x);
            if (x) {
                bs[i].set(j);
            }
        }
    }
    int k = 0;
    for (int i = 0; i < m; ++i) {
        int j = k;
        for (; j < n && !bs[j][i]; ++j);
        if (j == n) {
            continue;
        }
        std::swap(bs[j], bs[k]);
        for (j = k + 1; j < n; ++j) {
            if (bs[j][i]) {
                bs[j] ^= bs[k];
            }
        }
        ++k;
    }
    int ans = ((pow2[n] - pow2[n - k]) % mod + mod) % mod;
    ans = 1ll * ans * pow2[m - 1] % mod;
    printf("%d\n", ans);
    return 0;
}

### Prompt

In cpp, your task is to solve 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>

const int MAXN = 310;
const int mod = 998244353;

int n, m;
std::bitset<MAXN> bs[MAXN];
int pow2[MAXN];

int main() {
    pow2[0] = 1;
    for (int i = 1; i < MAXN; ++i) {
        pow2[i] = 2 * pow2[i - 1] % mod;
    }
    scanf("%d%d", &n, &m);
    for (int i = 0; i < n; ++i) {
        for (int j = 0, x; j < m; ++j) {
            scanf("%d", &x);
            if (x) {
                bs[i].set(j);
            }
        }
    }
    int k = 0;
    for (int i = 0; i < m; ++i) {
        int j = k;
        for (; j < n && !bs[j][i]; ++j);
        if (j == n) {
            continue;
        }
        std::swap(bs[j], bs[k]);
        for (j = k + 1; j < n; ++j) {
            if (bs[j][i]) {
                bs[j] ^= bs[k];
            }
        }
        ++k;
    }
    int ans = ((pow2[n] - pow2[n - k]) % mod + mod) % mod;
    ans = 1ll * ans * pow2[m - 1] % mod;
    printf("%d\n", ans);
    return 0;
}

```