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 MAXN = 300;
struct point {
  int x, y;
  point() {}
  point(const int _x, const int _y) : x(_x), y(_y) {}
} points[MAXN];
istream &operator>>(istream &in, point &p) {
  in >> p.x >> p.y;
  return in;
}
int operator^(const point a, const point b) { return a.x * b.y - a.y * b.x; }
point operator-(const point a, const point b) {
  return point(a.x - b.x, a.y - b.y);
}
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> points[i];
  }
  int max_result_area_sum = 0;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      point diagonal = points[j] - points[i];
      int max_positive_area = 0, min_negative_area = 0;
      for (int k = 0; k < n; k++) {
        if (k == i || k == j) {
          continue;
        }
        point side = points[k] - points[i];
        int current_area = side ^ diagonal;
        max_positive_area = max(max_positive_area, current_area);
        min_negative_area = min(min_negative_area, current_area);
      }
      if (max_positive_area > 0 && min_negative_area < 0) {
        max_result_area_sum =
            max(max_result_area_sum, max_positive_area - min_negative_area);
      }
    }
  }
  cout.precision(9);
  cout.setf(ios::fixed);
  cout << max_result_area_sum / 2.0L << endl;
  return 0;
}