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;
int n;
pair<int, int> a[1000];
double findarea(pair<int, int> a, pair<int, int> b, pair<int, int> c) {
  return ((double)a.first * (b.second - c.second) +
          (double)b.first * (c.second - a.second) +
          (double)c.first * (a.second - b.second)) /
         2.0;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%d %d", &a[i].first, &a[i].second);
  double ans = 0;
  for (int i = 0; i < n; i++)
    for (int j = i + 1; j < n; j++) {
      double maxright = -1, maxleft = -1;
      for (int k = 0; k < n; k++) {
        if (k != i && k != j) {
          double area = findarea(a[i], a[j], a[k]);
          if (area < 0)
            maxleft = max(maxleft, -area);
          else
            maxright = max(maxright, area);
        }
      }
      if (maxright >= 0 && maxleft >= 0) ans = max(ans, maxleft + maxright);
    }
  printf("%.6lf\n", ans);
  return 0;
}