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;
int main() {
  int n;
  vector<pair<int, int>> points;
  double ans = -1;
  cin >> n;
  for (int i = 0; i < n; i++) {
    int a, b;
    cin >> a >> b;
    points.push_back(make_pair(a, b));
  }
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      pair<int, int> fdp = points[i];
      pair<int, int> sdp = points[j];
      double maxt = -1;
      double mint = 1;
      for (int k = 0; k < n; k++) {
        if (k == i || k == j) continue;
        int kix = fdp.first - points[k].first;
        int kiy = fdp.second - points[k].second;
        int kjx = sdp.first - points[k].first;
        int kjy = sdp.second - points[k].second;
        double A = (kix * kjy - kiy * kjx + 0.0) / 2;
        maxt = max(maxt, A);
        mint = min(mint, A);
      }
      if (maxt <= 0 || mint >= 0)
        continue;
      else {
        ans = max(ans, maxt + abs(mint));
      }
    }
  }
  cout << fixed << setprecision(15) << ans << endl;
  return 0;
}