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[300], y[300];
int ans;
int main() {
  int i, j, k;
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d %d", x + i, y + i);
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      int l = 0, r = 0;
      for (k = 0; k < n; k++) {
        int cross =
            (x[j] - x[i]) * (y[k] - y[j]) - (y[j] - y[i]) * (x[k] - x[j]);
        l = min(l, cross);
        r = max(r, cross);
      }
      if (l < 0 && r > 0) ans = max(ans, r - l);
    }
  }
  printf("%lf\n", ans / 2.0);
}