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 p {
  int x, y;
} a[400];
int main() {
  int n, i, j, k;
  cin >> n;
  for (i = 0; i < n; i++) cin >> a[i].x >> a[i].y;
  double ans = 0;
  for (i = 0; i < n; i++) {
    for (j = 0; j < i; j++) {
      double l = 0, r = 0, ret;
      for (k = 0; k < n; k++)
        if (k != i && j != i) {
          ret = (a[j].x - a[i].x) * (a[i].y - a[k].y) -
                (a[i].x - a[k].x) * (a[j].y - a[i].y);
          ret /= 2;
          if (ret < 0) l = max(l, -ret);
          if (ret > 0) r = max(r, ret);
          if (l > 0 && r > 0) ans = max(ans, l + r);
        }
    }
  }
  std::cout << std::setprecision(15) << fixed << ans << endl;
}