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;
struct Point {
  double x, y;
} p[301];
inline double Area(Point &a, Point &b, Point &c) {
  return ((a.x - c.x) * (b.y - c.y) - (a.y - c.y) * (b.x - c.x)) / 2;
}
inline void check(double &a, double b) {
  if (b - a > 1e-10) a = b;
}
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; ++i) cin >> p[i].x >> p[i].y;
  double res = 0;
  for (int i = 0; i < n; ++i)
    for (int j = i + 1; j < n; ++j) {
      double Max1 = -1, Max2 = -1;
      for (int k = 0; k < n; ++k) {
        {
          if (k == i || k == j) continue;
        }
        if (Area(p[i], p[j], p[k]) < 0)
          check(Max1, -Area(p[i], p[j], p[k]));
        else
          check(Max2, Area(p[i], p[j], p[k]));
      }
      if (Max1 >= 0 && Max2 >= 0) check(res, Max1 + Max2);
    }
  cout << setiosflags(ios::fixed) << setprecision(6) << res << endl;
  return 0;
}