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>
typedef struct Point {
  int x, y;
} Point;
Point p[305];
double area(Point a, Point b, Point c) {
  return a.x * b.y - b.x * a.y + b.x * c.y - c.x * b.y + c.x * a.y - a.x * c.y;
}
double max(double s1, double s2) { return s1 > s2 ? s1 : s2; }
int main() {
  int n;
  while (scanf("%d", &n) != EOF) {
    int i, j, k;
    double s1, s2, s3, s;
    for (i = 0; i < n; i++) scanf("%d %d", &p[i].x, &p[i].y);
    s3 = 0;
    for (i = 0; i < n; i++) {
      for (j = i + 1; j < n; j++) {
        s1 = s2 = 0;
        for (k = 0; k < n; k++) {
          if (k != i && k != j) {
            s = area(p[i], p[k], p[j]);
            if (s > 0)
              s1 = max(s1, fabs(s) / 2);
            else if (s < 0)
              s2 = max(s2, fabs(s) / 2);
          }
        }
        if (s1 != 0 && s2 != 0) s3 = max(s1 + s2, s3);
      }
    }
    printf("%.6lf\n", s3);
  }
  return 0;
}