Problem: Iahub has drawn a set of n points in the cartesian plane which he calls "special points". A quadrilateral is a simple polygon without self-intersections with four sides (also called edges) and four vertices (also called corners). Please note that a quadrilateral doesn't have to be convex. A special quadrilateral is one which has all four vertices in the set of special points. Given the set of special points, please calculate the maximal area of a special quadrilateral. 

Input

The first line contains integer n (4 ≤ n ≤ 300). Each of the next n lines contains two integers: xi, yi ( - 1000 ≤ xi, yi ≤ 1000) — the cartesian coordinates of ith special point. It is guaranteed that no three points are on the same line. It is guaranteed that no two points coincide. 

Output

Output a single real number — the maximal area of a special quadrilateral. The answer will be considered correct if its absolute or relative error does't exceed 10 - 9.

Examples

Input

5
0 0
0 4
4 0
4 4
2 3


Output

16.000000

Note

In the test example we can choose first 4 points to be the vertices of the quadrilateral. They form a square by side 4, so the area is 4·4 = 16.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N = 300;
int n;
int x[N], y[N];
int det(int i, int j, int k) {
  return (x[j] - x[i]) * (y[k] - y[i]) - (y[j] - y[i]) * (x[k] - x[i]);
}
int main() {
  ios::sync_with_stdio(false), cin.tie(nullptr);
  cin >> n;
  for (int i = 0; i < (n); i++) cin >> x[i] >> y[i];
  long double ans = 0;
  for (int i = 0; i < (n); i++) {
    for (int j = i + 1; j < n; j++) {
      int cnt_u = 0, cnt_d = 0;
      int best_u = 0, best_d = 0;
      for (int k = 0; k < (n); k++)
        if (k != i && k != j) {
          int d = det(i, j, k);
          switch ((d > 0) - (d < 0)) {
            case +1:
              cnt_d++, best_d = max(best_d, +d);
              break;
            case 0:
              cnt_u++, cnt_d++;
              break;
            case -1:
              cnt_u++, best_u = max(best_u, -d);
              break;
          }
        }
      if (cnt_u && cnt_d) {
        ans = max(ans, (best_u + best_d) / 2.L);
      }
    }
  }
  cout << fixed << setprecision(10) << ans << '\n';
}