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 dara {
  double x, y;
} a[310];
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i].x >> a[i].y;
  double fn = -INT_MAX;
  for (int i = 1; i <= n; i++) {
    for (int j = i + 1; j <= n; j++) {
      double mx = -INT_MAX, mn = INT_MAX;
      for (int k = 1; k <= n; k++) {
        if (i != k && j != k) {
          double tmp =
              0.5 * (a[i].x * (a[j].y - a[k].y) + a[j].x * (a[k].y - a[i].y) +
                     a[k].x * (a[i].y - a[j].y));
          mx = max(mx, tmp);
          mn = min(mn, tmp);
        }
      }
      fn = max(fn, mx + (-1 * mn));
    }
  }
  printf("%.9lf\n", fn);
}