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;
double ccw(pair<int, int> a, pair<int, int> b, pair<int, int> c) {
  return 0.5 * ((double)((b.first - a.first) * (c.second - a.second) -
                         (c.first - a.first) * (b.second - a.second)));
}
int main() {
  int n, x, y;
  double maxArea = INT_MIN;
  vector<pair<int, int>> v;
  scanf("%i", &n);
  for (int i = 0; i < n; ++i) {
    scanf("%i %i", &x, &y);
    v.push_back(make_pair(x, y));
  }
  for (int i = 0; i < n - 1; ++i) {
    pair<int, int> a = v[i];
    for (int j = i + 1; j < n; ++j) {
      pair<int, int> b = v[j];
      double posMax = INT_MIN, negMax = INT_MAX;
      bool p = false;
      bool ne = false;
      pair<int, int> pos, neg;
      for (int k = 0; k < n; ++k) {
        if (k != i && k != j) {
          pair<int, int> c = v[k];
          if (ccw(a, b, c) > 0 && ccw(a, b, c) > posMax) {
            p = true;
            pos = c;
            posMax = ccw(a, b, c);
          }
          if (ccw(a, b, c) < 0 && (!ne || ccw(a, b, c) < negMax)) {
            ne = true;
            neg = c;
            negMax = ccw(a, b, c);
          }
        }
      }
      if ((ne && p) && (fabs(negMax) + posMax) > maxArea)
        maxArea = (fabs(negMax) + posMax);
    }
  }
  printf("%lf", maxArea);
  return 0;
}