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

const int mod = 998244353;

int x[205], y[205];
long long p2[205];

bool linear(int i, int j, int k) {
  return (y[j] - y[i]) * (x[k] - x[i]) == (y[k] - y[i]) * (x[j] - x[i]);
}

int main() {
  long long t = 1;
  for (int i = 0; i <= 200; i++) {
    p2[i] = t;
    t *= 2;
    t %= mod;
  }
  int n;
  cin >> n;
  for (int ni = 0; ni < n; ni++) {
    cin >> x[ni] >> y[ni];
  }
  if (n < 3) {
    cout << 0 << endl;
    return 0;
  }
  long long ans = 0;
  for (int ni = 0; ni < n; ni++) {
    for (int nj = ni + 1; nj < n; nj++) {
      bool feasible = true;
      for (int nk = 0; nk < nj; nk++) {
        if (nk == ni) continue;
        if (linear(ni, nj, nk)) {
          feasible = false;
          break;
        }
      }
      if (!feasible) continue;
      int cnt = 2;
      for (int nk = nj + 1; nk < n; nk++) {
        if (linear(ni, nj, nk)) cnt++;
      }
      ans += p2[cnt] - 1 - cnt - cnt * (cnt - 1) / 2 + mod;
      ans %= mod;
    }
  }
  ans = p2[n] - 1 - n - n * (n - 1) / 2 - ans + mod;
  ans %= mod;
  cout << ans << endl;
  return 0;
}
### Prompt

Your task is to create a cpp solution to the following problem:

You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.

cddb0c267926c2add885ca153c47ad8a.png

For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.

For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.

Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.

However, since the sum can be extremely large, print the sum modulo 998244353.

Constraints

* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.

Input

The input is given from Standard Input in the following format:


N
x_1 y_1
x_2 y_2
:
x_N y_N


Output

Print the sum of all the scores modulo 998244353.

Examples

Input

4
0 0
0 1
1 0
1 1


Output

5


Input

5
0 0
0 1
0 2
0 3
1 1


Output

11


Input

1
3141 2718


Output

0

### Response

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

const int mod = 998244353;

int x[205], y[205];
long long p2[205];

bool linear(int i, int j, int k) {
  return (y[j] - y[i]) * (x[k] - x[i]) == (y[k] - y[i]) * (x[j] - x[i]);
}

int main() {
  long long t = 1;
  for (int i = 0; i <= 200; i++) {
    p2[i] = t;
    t *= 2;
    t %= mod;
  }
  int n;
  cin >> n;
  for (int ni = 0; ni < n; ni++) {
    cin >> x[ni] >> y[ni];
  }
  if (n < 3) {
    cout << 0 << endl;
    return 0;
  }
  long long ans = 0;
  for (int ni = 0; ni < n; ni++) {
    for (int nj = ni + 1; nj < n; nj++) {
      bool feasible = true;
      for (int nk = 0; nk < nj; nk++) {
        if (nk == ni) continue;
        if (linear(ni, nj, nk)) {
          feasible = false;
          break;
        }
      }
      if (!feasible) continue;
      int cnt = 2;
      for (int nk = nj + 1; nk < n; nk++) {
        if (linear(ni, nj, nk)) cnt++;
      }
      ans += p2[cnt] - 1 - cnt - cnt * (cnt - 1) / 2 + mod;
      ans %= mod;
    }
  }
  ans = p2[n] - 1 - n - n * (n - 1) / 2 - ans + mod;
  ans %= mod;
  cout << ans << endl;
  return 0;
}
```