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;
int n, x[310], y[310];
int cross(int x1, int y1, int x2, int y2) { return x1 * y2 - x2 * y1; }
int main() {
  int i, j, k, maxn, minn, ans = 0;
  cin >> n;
  for (i = 1; i <= n; i++) scanf("%d%d", &x[i], &y[i]);
  for (i = 1; i <= n; i++)
    for (j = i + 1; j <= n; j++) {
      for (maxn = -(int)1e9, minn = (int)1e9, k = 1; k <= n; k++)
        if (k != i && k != j) {
          int s = cross(x[i] - x[k], y[i] - y[k], x[j] - x[k], y[j] - y[k]);
          maxn = max(maxn, s);
          minn = min(minn, s);
        }
      ans = max(ans, maxn - minn);
    }
  printf("%lf", (double)ans / 2);
  return 0;
}