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 N = 300 + 5;
inline double CrossMulti(const complex<double> &a, const complex<double> &b) {
  return (conj(a) * b).imag();
}
int main() {
  int n;
  complex<double> a[N];
  while (cin >> n) {
    double x, y;
    for (int i = 0; i < n; i++) {
      cin >> x >> y;
      a[i] = complex<double>(x, y);
    }
    double ans = 0;
    for (int i = 0; i < n; i++) {
      for (int j = i + 1; j < n; j++) {
        double Min = 1e100, Max = -1e100;
        for (int k = 0; k < n; k++)
          if (k != i && k != j) {
            double tmp = CrossMulti(a[j] - a[i], a[k] - a[i]);
            Min = min(Min, tmp);
            Max = max(Max, tmp);
          }
        if (Min * Max < 0) ans = max(ans, abs(Max) + abs(Min));
      }
    }
    ans *= 0.5;
    printf("%.4lf\n", ans);
  }
}