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;
const int A = 5e5 + 2;
const int mod = 1e9 + 7;
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n;
  cin >> n;
  vector<complex<double> > v;
  for (int i = 0; i < n; i++) {
    int x, y;
    cin >> x >> y;
    v.push_back(complex<double>(x, y));
  }
  double ans = 0;
  for (int i = 0; i < n; i++) {
    complex<double> p1 = v[i], p2, p3;
    for (int j = i + 1; j < n; j++) {
      p2 = v[j];
      double area1 = -1, area2 = -1, c_p;
      for (int k = 0; k < n; k++) {
        if (i == k || j == k) continue;
        p3 = v[k];
        c_p = (conj((p2) - (p1)) * ((p3) - (p1))).imag();
        if (c_p > 1e-6) area1 = max(area1, c_p / 2.0);
        if (c_p < -1e-6) area2 = max(area2, -c_p / 2.0);
      }
      if (area1 > -1e-6 && area2 > -1e-6) ans = max(ans, area1 + area2);
    }
  }
  cout << fixed << setprecision(9) << ans;
  return 0;
}