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;
};
double ccw(point &a, point &b, point &c) {
  return double(b.x - a.x) * (c.y - b.y) - double(b.y - a.y) * (c.x - b.x);
}
int main() {
  double maxArea = 0;
  int i, j, k;
  int n;
  cin >> n;
  vector<struct point> points(n);
  for (i = 0; i < n; ++i) {
    cin >> points[i].x >> points[i].y;
  }
  for (i = 0; i < n; ++i) {
    for (j = 0; j < n; ++j) {
      double maxMinus = -1, maxPlus = -1;
      double area;
      if (j == i) continue;
      for (k = 0; k < n; ++k) {
        if (k == j || k == i) continue;
        area = ccw(points[i], points[j], points[k]);
        if (area < 0) {
          maxMinus = max(-area, maxMinus);
        } else {
          maxPlus = max(area, maxPlus);
        }
      }
      if (maxMinus > 0 && maxPlus > 0)
        maxArea = max(maxArea, maxMinus + maxPlus);
    }
  }
  printf("%lf\n", maxArea / 2);
  return 0;
}