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 cross(pair<int, int> A, pair<int, int> B, pair<int, int> C) {
  double tmp;
  tmp = ((B.first - A.first) * (C.second - B.second) -
         (C.first - B.first) * (B.second - A.second));
  tmp = tmp * 0.5;
  return tmp;
}
pair<int, int> p[500];
double area, maxminus, maxplus, tmp;
int main() {
  int n;
  cin >> n;
  area = 0;
  for (int i = 1; i <= n; i++) {
    cin >> p[i].first >> p[i].second;
  }
  for (int i = 1; i <= n; i++) {
    for (int j = i + 1; j <= n; j++) {
      maxminus = -1;
      maxplus = -1;
      for (int k = 1; k <= n; k++) {
        if (k == i || k == j) continue;
        tmp = cross(p[i], p[j], p[k]);
        if (tmp <= 0) {
          maxminus = max(maxminus, -tmp);
        } else {
          maxplus = max(maxplus, tmp);
        }
      }
      if (maxplus >= 0 && maxminus >= 0) area = max(area, maxplus + maxminus);
    }
  }
  cout << fixed << setprecision(12) << area << endl;
}