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 a[100010], b[100000];
int main() {
  int n, res = -1;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i] >> b[i];
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      int x = 0, y = 0;
      for (int k = 0; k < n; k++) {
        int f = (a[j] - a[i]) * (b[k] - b[j]) - (b[j] - b[i]) * (a[k] - a[j]);
        x = min(x, f);
        y = max(y, f);
      }
      if (x < 0 && y > 0) res = max(res, y - x);
    }
  }
  cout << fixed << setprecision(9) << res / 2.0 << endl;
}