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 {
  double x;
  double y;
  point(double x, double y) {
    this->x = x;
    this->y = y;
  }
};
double crossproduct(point *a, point *b, point *c) {
  double ans = 0.0;
  ans += ((b->x) - (a->x)) * ((c->y) - (a->y));
  ans -= ((c->x) - (a->x)) * ((b->y) - (a->y));
  return ans / 2.0;
}
int main() {
  int n;
  cin >> n;
  point **points = new point *[n];
  int x, y;
  for (int i = 0; i < n; i++) {
    cin >> x >> y;
    points[i] = new point(x, y);
  }
  double max_area = 0.0;
  double crossp = 0.0;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      double max_positive = -1;
      double max_negative = -1;
      bool positive_found = false, negative_found = false;
      for (int k = 0; k < n; k++) {
        if (k == i || k == j) continue;
        crossp = crossproduct(points[i], points[j], points[k]);
        if (crossp > 0.0) {
          max_positive = max(max_positive, crossp);
          positive_found = true;
        } else {
          max_negative = max(max_negative, -1.0 * crossp);
          negative_found = true;
        }
      }
      if (positive_found && negative_found) {
        max_area = max(max_area, max_positive + max_negative);
      }
    }
  }
  printf("%.12lf\n", max_area);
}