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;
inline double chmax(double &A, double B) {
  if (B - A > 0.00000001) A = B;
}
int main() {
  int n;
  cin >> n;
  double x, y, max_area = 0, area;
  vector<pair<double, double>> q;
  for (int i = 0; i < n; i++) {
    cin >> x >> y;
    q.push_back(make_pair(x, y));
  }
  double area_p, area_n;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      area_p = -1;
      area_n = -1;
      for (int k = 0; k < n; k++) {
        if (k != i && k != j) {
          double ccp =
              (double)((q[k].first - q[i].first) * (q[j].second - q[k].second) -
                       (q[j].first - q[k].first) *
                           (q[k].second - q[i].second)) *
              0.5;
          if (ccp > 0)
            chmax(area_p, ccp);
          else
            chmax(area_n, -ccp);
        }
      }
      if (area_p >= 0 && area_n >= 0)
        if (max_area < (area_p + area_n))
          chmax(max_area, area_p + area_n);
        else
          continue;
    }
  }
  cout << fixed;
  cout << setprecision(6) << max_area;
  return 0;
}