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 n, x, y;
complex<double> a[302];
double b, c, ans;
int main() {
  cin >> n;
  for (int i = (1); i <= (int)(n); i++) {
    scanf("%d %d", &x, &y);
    a[i] = complex<double>(x, y);
  }
  for (int i = (1); i <= (int)(n); i++)
    for (int j = (i + 1); j <= (int)(n); j++) {
      c = b = -1;
      for (int k = (1); k <= (int)(n); k++) {
        if (k == i || k == j) continue;
        if ((((conj(((a[j]) - (a[i]))) * (((a[k]) - (a[i])))).imag()) > 1e-6))
          c = max(c, 0.5 * fabs(((conj(((a[j]) - (a[i]))) * (((a[k]) - (a[j]))))
                                     .imag())));
        else
          b = max(b, 0.5 * fabs(((conj(((a[j]) - (a[i]))) * (((a[k]) - (a[j]))))
                                     .imag())));
      }
      if (c >= 0 && b >= 0) ans = max(ans, c + b);
    }
  printf("%.9f", ans);
}