#include <bits/stdc++.h>
using namespace std;
using UL = unsigned int;
using ULL = unsigned long long;
using LL = long long;
#define rep(i, n) for(UL i = 0; i < (n); i++)

struct Problem {

    UL G[300][300];

    static const ULL M = 998244353;

    void Solve() {
        UL H, W; scanf("%d%d", &H, &W);
        rep(y, H) rep(x, W) {
            char c; scanf(" %c", &c);
            G[x][y] = c - '0';
        }
        UL Ker = 0;
        UL K = 0;
        rep(y, H) {
            UL Y = 0;
            while (true) {
                if (K == W) break;
                for (Y = y; Y < H; Y++) if (G[K][Y]) break;
                if (Y < H) break;
                K++;
            }
            if (K == W) { Ker = H - y; break; }
            rep(x, W) swap(G[x][y], G[x][Y]);
            for (UL yy = y + 1; yy < H; yy++) {
                if (G[K][yy]) {
                    for (UL x = K; x < W; x++)
                        G[x][yy] = G[x][yy] ^ G[x][y];
                }
            }
        }
        ULL ans = 1; rep(i, H + W - 1) ans = ans * 2 % M;
        ULL sub = 1; rep(i, Ker + W - 1) sub = sub * 2 % M;
        ans = (ans + M - sub) % M;
        cout << ans << endl;
    }
};
int main() {
    unique_ptr<Problem> p(new Problem());
    //cout << fixed << setprecision(10);
    p->Solve();
    return 0;
}

### Prompt

Create a solution in cpp for 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;
using UL = unsigned int;
using ULL = unsigned long long;
using LL = long long;
#define rep(i, n) for(UL i = 0; i < (n); i++)

struct Problem {

    UL G[300][300];

    static const ULL M = 998244353;

    void Solve() {
        UL H, W; scanf("%d%d", &H, &W);
        rep(y, H) rep(x, W) {
            char c; scanf(" %c", &c);
            G[x][y] = c - '0';
        }
        UL Ker = 0;
        UL K = 0;
        rep(y, H) {
            UL Y = 0;
            while (true) {
                if (K == W) break;
                for (Y = y; Y < H; Y++) if (G[K][Y]) break;
                if (Y < H) break;
                K++;
            }
            if (K == W) { Ker = H - y; break; }
            rep(x, W) swap(G[x][y], G[x][Y]);
            for (UL yy = y + 1; yy < H; yy++) {
                if (G[K][yy]) {
                    for (UL x = K; x < W; x++)
                        G[x][yy] = G[x][yy] ^ G[x][y];
                }
            }
        }
        ULL ans = 1; rep(i, H + W - 1) ans = ans * 2 % M;
        ULL sub = 1; rep(i, Ker + W - 1) sub = sub * 2 % M;
        ans = (ans + M - sub) % M;
        cout << ans << endl;
    }
};
int main() {
    unique_ptr<Problem> p(new Problem());
    //cout << fixed << setprecision(10);
    p->Solve();
    return 0;
}

```