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;
typedef struct {
  int x, y;
} point;
double absf(double a) { return (a < 0 ? -a : a); }
int main() {
  int n;
  cin >> n;
  point a[n];
  for (int i = 0; i < n; ++i) cin >> a[i].x >> a[i].y;
  double s = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if (i == j) continue;
      double mn = 1e9, mx = -1e9, p = 0;
      int mn_id = 0, mx_id = 0;
      for (int k = 0; k < n; ++k) {
        if (k == i || k == j) continue;
        p = (a[i].x - a[k].x) * (a[j].y - a[k].y) -
            (a[i].y - a[k].y) * (a[j].x - a[k].x);
        if (mn > p) {
          mn = p;
          mn_id = k;
        }
        if (mx < p) {
          mx = p;
          mx_id = k;
        }
      }
      if (mn_id != mx_id) s = max(s, absf(mx - mn));
    }
  }
  s /= 2;
  cout.precision(20);
  cout << s;
  return 0;
}