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 MAXN = 305;
pair<int, int> a[MAXN];
int main() {
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  for (int i = 0; i < n; ++i) cin >> a[i].first >> a[i].second;
  double ans = 0;
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < n; ++j) {
      int gt = 0, ls = 0;
      for (int k = 0; k < n; ++k) {
        int c = (a[j].first - a[i].first) * (a[k].second - a[j].second) -
                (a[j].second - a[i].second) * (a[k].first - a[j].first);
        if (c > 0)
          gt = max(gt, c);
        else
          ls = min(ls, c);
      }
      if (ls && gt) ans = max(ans, 0. + -ls + gt);
    }
  cout.setf(ios::fixed);
  cout.precision(9);
  cout << ans / 2 << endl;
  return 0;
}