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 node {
  int x, y;
} op[310];
int cal(node a, node b, node c) {
  return (b.x - a.x) * (c.y - a.y) - (c.x - a.x) * (b.y - a.y);
}
int main() {
  int n, i, j, k, ans, maxn, minn, tmp;
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d%d", &op[i].x, &op[i].y);
  ans = 0;
  for (i = 0; i < n; i++)
    for (j = i + 1; j < n; j++) {
      maxn = minn = 0;
      for (k = 0; k < n; k++) {
        tmp = cal(op[i], op[j], op[k]);
        maxn = max(maxn, tmp);
        minn = min(minn, tmp);
      }
      if (maxn != 0 && minn != 0) ans = max(ans, maxn - minn);
    }
  printf("%.9lf", (double)ans / 2);
  return 0;
}