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;
inline void chechMax(double &x, double y) { x = x < y ? y : x; }
struct Point {
  double x, y;
} a[310];
inline double ccw(const Point &p1, const Point &p2, const Point &p3) {
  return (p2.x - p1.x) * (p3.y - p1.y) - (p2.y - p1.y) * (p3.x - p1.x);
}
int main(int argc, char const *argv[]) {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) scanf("%lf%lf", &a[i].x, &a[i].y);
  double res = 0;
  for (int i = 0; i < n; ++i)
    for (int j = i + 1; j < n; ++j) {
      bool f1 = true, f2 = true;
      double t1 = -1, t2 = -1;
      for (int k = 0; k < n; ++k)
        if (k != i && k != j) {
          double tmp = ccw(a[i], a[j], a[k]);
          if (tmp > 0) t1 = max(t1, abs(tmp)), f1 = false;
          if (tmp < 0) t2 = max(t2, abs(tmp)), f2 = false;
        }
      if (f1 || f2) continue;
      chechMax(res, 0.5 * (t1 + t2));
    }
  cout << fixed << setprecision(12) << res << "\n";
  return 0;
}