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 area = 0, pos_loc = 0, neg_loc = 0;
void ccw(pair<int, int> a, pair<int, int> b, pair<int, int> c) {
  double d = (double)((b.first - a.first) * (c.second - b.second) * 1.0 -
                      (b.second - a.second) * (c.first - b.first) * 1.0) *
             0.5;
  if (d < 0 && neg_loc < abs(d))
    neg_loc = abs(d);
  else if (d > 0 && pos_loc < abs(d))
    pos_loc = abs(d);
}
int main() {
  int n;
  pair<int, int> p[310];
  cin >> n;
  for (int i = 0; i < n; i++) cin >> p[i].first >> p[i].second;
  for (int i = 0; i < n - 1; i++) {
    for (int j = i + 1; j < n; j++) {
      pos_loc = neg_loc = 0;
      for (int k = 0; k < n; k++) {
        if (k != i && k != j) {
          ccw(p[i], p[j], p[k]);
        }
      }
      if (pos_loc && neg_loc) {
        if (pos_loc + neg_loc > area) area = pos_loc + neg_loc;
      }
    }
  }
  cout << fixed << setprecision(12) << area << endl;
}