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;
} point[400];
double across(Point a, Point b, Point c) {
  return ((a.x - c.x) * (b.y - c.y) - (b.x - c.x) * (a.y - c.y)) / 2;
}
int main() {
  int n;
  double ans = 0, lmax, rmax;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> point[i].x >> point[i].y;
  }
  for (int i = 1; i <= n; i++) {
    for (int j = i + 1; j <= n; j++) {
      lmax = 0;
      rmax = 0;
      for (int k = 1; k < n; k++) {
        if (k == i || k == j) {
          continue;
        }
        double s = across(point[i], point[j], point[k]);
        if (s < 0) {
          lmax = max(lmax, -s);
        } else {
          rmax = max(rmax, s);
        }
      }
      if (lmax == 0 || rmax == 0) {
        continue;
      }
      ans = max(ans, (lmax + rmax));
    }
  }
  printf("%lf\n", ans);
  return 0;
}