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() {}
  Point(int _x, int _y) : x(_x), y(_y) {}
  void get() { scanf("%lf%lf", &x, &y); }
} a[100005];
inline double xmult(const Point& p1, const Point& p2, const Point& p0) {
  return (p1.x - p0.x) * (p2.y - p0.y) - (p2.x - p0.x) * (p1.y - p0.y);
}
int n;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) a[i].get();
  double Max = 0;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if (i == j) continue;
      double MaxL = 0, MaxR = 0;
      for (int k = 1; k <= n; k++) {
        if (k == i || k == j) continue;
        double tmp = xmult(a[i], a[j], a[k]);
        tmp /= 2;
        if (tmp < 0) {
          MaxL = max(MaxL, -tmp);
        } else {
          MaxR = max(MaxR, tmp);
        }
        if (MaxL > 0 && MaxR > 0) Max = max(Max, MaxL + MaxR);
      }
    }
  }
  printf("%lf\n", Max);
  return 0;
}