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 Coord {
  int x, y;
  Coord(int a = 0, int b = 0) {
    x = a;
    y = b;
  }
  bool operator==(const Coord c) const { return c.x == x && c.y == y; }
};
double area(Coord &A, Coord &B, Coord &C) {
  return (double)(A.x * (B.y - C.y) + B.x * (C.y - A.y) + C.x * (A.y - B.y)) *
         0.5;
}
int main() {
  int n;
  cin >> n;
  vector<Coord> points(n);
  for (int i = 0; i < n; i++) {
    int a, b;
    cin >> a >> b;
    points[i] = Coord(a, b);
  }
  double ret = 0;
  for (int i = 0; i < points.size(); i++) {
    for (int j = i + 1; j < points.size(); j++) {
      double right = 0, left = 0;
      for (int k = 0; k < points.size(); k++) {
        double dir = area(points[i], points[j], points[k]);
        if (dir > 0.0000000001)
          left = ((dir < left) ? left : dir);
        else if (dir < 0) {
          dir *= -1;
          right = ((dir < right) ? right : dir);
        }
      }
      if (right > 0 && left > 0) {
        right = right + left;
        ret = ((ret < right) ? right : ret);
      }
    }
  }
  cout << fixed << std::setprecision(9) << ret << endl;
}