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, y;
} z[301];
double cross(Point o, Point a, Point b) {
  return ((a.x - o.x) * (b.y - a.y) - (b.x - a.x) * (a.y - o.y)) / 2.0;
}
void maxc(double &a, double b) {
  if (b - a > 0.00000001) a = b;
}
int main() {
  int n;
  double t, maxArea = 0.0, positive = 0.0, negative = 0.0;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%lf %lf", &z[i].x, &z[i].y);
  for (int i = 0; i < n; i++)
    for (int j = i + 1; j < n; j++) {
      positive = -1.0;
      negative = -1.0;
      for (int k = 0; k < n; k++)
        if (i != k && j != k) {
          t = cross(z[i], z[j], z[k]);
          if (t < 0)
            maxc(negative, -t);
          else
            maxc(positive, t);
        }
      if (positive >= 0 && negative >= 0) maxc(maxArea, positive + negative);
    }
  printf("%lf", maxArea);
}