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 {
  int x;
  int y;
  point(int _x, int _y) : x(_x), y(_y) {}
};
using std::fixed;
int main() {
  ios_base::sync_with_stdio(0);
  int n;
  cin >> n;
  vector<point> V;
  for (int i = (1); i <= (n); ++i) {
    int x, y;
    cin >> x >> y;
    V.push_back(point(x, y));
  }
  int ans = 0;
  for (int i = (0); i <= (n - 1); ++i)
    for (int j = (i + 1); j <= (n - 1); ++j) {
      int max_area = -1000000001, min_area = 1000000001;
      for (int k = (0); k <= (n - 1); ++k)
        if ((k != i) && (k != j)) {
          max_area =
              (((max_area) >
                ((V[i].x * V[j].y + V[i].y * V[k].x + V[k].y * V[j].x -
                  V[j].y * V[k].x - V[k].y * V[i].x - V[i].y * V[j].x)))
                   ? (max_area)
                   : ((V[i].x * V[j].y + V[i].y * V[k].x + V[k].y * V[j].x -
                       V[j].y * V[k].x - V[k].y * V[i].x - V[i].y * V[j].x)));
          min_area =
              (((min_area) <
                ((V[i].x * V[j].y + V[i].y * V[k].x + V[k].y * V[j].x -
                  V[j].y * V[k].x - V[k].y * V[i].x - V[i].y * V[j].x)))
                   ? (min_area)
                   : ((V[i].x * V[j].y + V[i].y * V[k].x + V[k].y * V[j].x -
                       V[j].y * V[k].x - V[k].y * V[i].x - V[i].y * V[j].x)));
        }
      if (max_area >= 0 && min_area <= 0)
        ans = (((ans) > (max_area - min_area)) ? (ans) : (max_area - min_area));
    }
  double d = (ans / 2.0);
  cout << fixed;
  cout << d;
  return 0;
}