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;
ifstream in("maximal_area_quadrilateral.in");
ofstream out("maximal_area_quadrilateral.out");
struct punct {
  int x;
  int y;
};
int intoarcere(punct A, punct B, punct C) {
  return (B.x - A.x) * (C.y - A.y) - (C.x - A.x) * (B.y - A.y);
}
int main() {
  int n, maxim = 0;
  cin.sync_with_stdio(false);
  cin >> n;
  vector<punct> v(n + 1);
  for (int i = 1; i <= n; i++) cin >> v[i].x >> v[i].y;
  for (int i = 1; i < n; i++)
    for (int j = i + 1; j <= n; j++) {
      int max_st = -1;
      int max_dr = -1;
      for (int w = 1; w <= n; w++) {
        if (w == i || w == j) continue;
        int val = intoarcere(v[i], v[j], v[w]);
        if (val < 0)
          max_st = max(max_st, -val);
        else
          max_dr = max(max_dr, val);
      }
      if (max_st != -1 && max_dr != -1) maxim = max(maxim, max_st + max_dr);
    }
  cout << fixed << setprecision(1) << double(maxim) / 2;
  return 0;
}