#include <cstdio>
#include <cstring>
#include <vector>
#include <algorithm>

const int MOD = 998244353;
const int kN = 300 + 5;
int n, m;
int a[kN][kN];

int power(int a, int b) {
  int ret = 1;
  while (b) {
    if (b & 1) ret = ret * 1LL * a % MOD;
    a = a * 1LL * a % MOD;
    b >>= 1;
  }
  return ret;
}

int gauss() {
  int ret = 0;
  for (int i = 0, p = 0; i < n; ++ i) {
    int k = -1;
    while (k == -1 && p != m) {
      for (int j = i; j < n; ++ j) {
        if (a[j][p]) {
          k = j;
          break;
        }
      }
      if (k == -1) {
        ++ p;
      }
    }
    if (k == -1) break;
    ret ++;
    for (int r = 0; r < m; ++ r)
      std::swap(a[i][r], a[k][r]);
    for (int w = i + 1; w < n; ++ w) {
      if (a[w][p]) {
        for (int r = 0; r < m; ++ r)
          a[w][r] ^= a[i][r];
      }
    }
    ++ p;
  }
  return ret;
}

int main() {
  scanf("%d%d", &n, &m);
  for (int i = 0; i < n; ++ i) {
    for (int j = 0; j < m; ++ j) {
      scanf("%d", &a[i][j]);
    }
  }
  int rank = gauss();
  int result = (power(2, n) - power(2, n - rank) + MOD) % MOD * 1LL * power(2, m - 1) % MOD;
  printf("%d\n", result);
}

### 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 <cstdio>
#include <cstring>
#include <vector>
#include <algorithm>

const int MOD = 998244353;
const int kN = 300 + 5;
int n, m;
int a[kN][kN];

int power(int a, int b) {
  int ret = 1;
  while (b) {
    if (b & 1) ret = ret * 1LL * a % MOD;
    a = a * 1LL * a % MOD;
    b >>= 1;
  }
  return ret;
}

int gauss() {
  int ret = 0;
  for (int i = 0, p = 0; i < n; ++ i) {
    int k = -1;
    while (k == -1 && p != m) {
      for (int j = i; j < n; ++ j) {
        if (a[j][p]) {
          k = j;
          break;
        }
      }
      if (k == -1) {
        ++ p;
      }
    }
    if (k == -1) break;
    ret ++;
    for (int r = 0; r < m; ++ r)
      std::swap(a[i][r], a[k][r]);
    for (int w = i + 1; w < n; ++ w) {
      if (a[w][p]) {
        for (int r = 0; r < m; ++ r)
          a[w][r] ^= a[i][r];
      }
    }
    ++ p;
  }
  return ret;
}

int main() {
  scanf("%d%d", &n, &m);
  for (int i = 0; i < n; ++ i) {
    for (int j = 0; j < m; ++ j) {
      scanf("%d", &a[i][j]);
    }
  }
  int rank = gauss();
  int result = (power(2, n) - power(2, n - rank) + MOD) % MOD * 1LL * power(2, m - 1) % MOD;
  printf("%d\n", result);
}

```