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;
struct point {
  int x;
  int y;
  bool operator!=(point &p1) const {
    if (x == p1.x && y == p1.y)
      return false;
    else
      return true;
  }
};
point ps[305];
int n;
int cross_product(point p0, point p1, point p2) {
  return (p1.x - p0.x) * (p2.y - p0.y) - (p1.y - p0.y) * (p2.x - p0.x);
}
int dir(point p0, point p1, point p2) {
  int temp = cross_product(p0, p1, p2);
  if (temp > 0)
    return 1;
  else if (temp < 0)
    return -1;
  else if (temp = 0)
    return 0;
}
double area(point p1, point p2, point p3) {
  return cross_product(p1, p2, p3) * 1.0 / 2;
}
double ans(point p1, point p2) {
  double positive_area_max = 0;
  double negative_area_max = 0;
  int p_count = 0;
  int n_count = 0;
  for (int i = 1; i <= n; i++) {
    if (ps[i] != p1 && ps[i] != p2) {
      if (dir(p1, p2, ps[i]) < 0) {
        p_count++;
        positive_area_max = max(positive_area_max, area(p1, ps[i], p2));
      } else if (dir(p1, p2, ps[i]) > 0) {
        n_count++;
        negative_area_max = max(negative_area_max, -area(p1, ps[i], p2));
      }
    }
  }
  if (p_count == 0 || n_count == 0) return 0;
  return positive_area_max + negative_area_max;
}
int main() {
  ios::sync_with_stdio(false);
  while (cin >> n) {
    for (int i = 1; i <= n; i++) {
      cin >> ps[i].x >> ps[i].y;
    }
    double max_area = 0;
    for (int i = 1; i <= n; i++) {
      for (int j = i + 1; j <= n; j++) {
        max_area = max(max_area, ans(ps[i], ps[j]));
      }
    }
    cout << fixed << setprecision(6) << max_area << endl;
  }
}