#include <bits/stdc++.h>

using namespace std;

const int max_n = 303, mod = 998244353;

int n, m;
bitset<max_n> b;
vector<bitset<max_n>> v;

int power(int n) {
    int res = 1;
    for (int i = 0; i < n; ++i) {
        res *= 2;
        res %= mod;
    }
    return res;
}

bool operator < (const bitset<max_n> &a, const bitset<max_n> &b) {
    for (int i = 0; i < m; ++i) {
        if (a[i] != b[i]) {
            return a[i] < b[i];
        }
    }
    return false;
}

void add(bitset<max_n> b) {
    for (int i = 0; i < v.size(); ++i) {
        if ((b ^ v[i]) < b) {
            b ^= v[i];
        }
    }
    if (b == 0) {
        return;
    }
    for (int i = 0; i < v.size(); ++i) {
        if ((b ^ v[i]) < v[i]) {
            v[i] ^= b;
        }
    }
    v.push_back(b);
}

int main() {
    //freopen("input.txt", "r", stdin);
    //freopen("output.txt", "w", stdout);
    cin >> n >> m;
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < m; ++j) {
            int x;
            cin >> x;
            b[j] = x;
        }
        add(b);
    }
    int ans = (power(n) + mod - power(n - v.size())) % mod;
    ans = 1LL * ans * power(m - 1) % mod;
    cout << ans << endl;
    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;

const int max_n = 303, mod = 998244353;

int n, m;
bitset<max_n> b;
vector<bitset<max_n>> v;

int power(int n) {
    int res = 1;
    for (int i = 0; i < n; ++i) {
        res *= 2;
        res %= mod;
    }
    return res;
}

bool operator < (const bitset<max_n> &a, const bitset<max_n> &b) {
    for (int i = 0; i < m; ++i) {
        if (a[i] != b[i]) {
            return a[i] < b[i];
        }
    }
    return false;
}

void add(bitset<max_n> b) {
    for (int i = 0; i < v.size(); ++i) {
        if ((b ^ v[i]) < b) {
            b ^= v[i];
        }
    }
    if (b == 0) {
        return;
    }
    for (int i = 0; i < v.size(); ++i) {
        if ((b ^ v[i]) < v[i]) {
            v[i] ^= b;
        }
    }
    v.push_back(b);
}

int main() {
    //freopen("input.txt", "r", stdin);
    //freopen("output.txt", "w", stdout);
    cin >> n >> m;
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < m; ++j) {
            int x;
            cin >> x;
            b[j] = x;
        }
        add(b);
    }
    int ans = (power(n) + mod - power(n - v.size())) % mod;
    ans = 1LL * ans * power(m - 1) % mod;
    cout << ans << endl;
    return 0;
}

```