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 {
  double x, y;
} a[310];
double f(int i, int j, int k) {
  return (a[k].x * (a[i].y - a[j].y) + a[j].x * (a[k].y - a[i].y) +
          a[i].x * (a[j].y - a[k].y)) /
         2.0;
}
int main() {
  int n, i, j, k;
  double smax = -10000000000, xmax = -10000000000, ans = -10000000000, temp;
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> a[i].x >> a[i].y;
  }
  for (i = 1; i <= n; i++) {
    for (j = 1; j <= n; j++) {
      if (j == i) continue;
      smax = -10000000000;
      xmax = -10000000000;
      for (k = 1; k <= n; k++) {
        if (k == i || k == j) continue;
        temp = f(i, j, k);
        if (temp < 0) {
          smax = max(smax, -temp);
        } else {
          xmax = max(xmax, temp);
        }
      }
      ans = max(ans, smax + xmax);
    }
  }
  printf("%.6lf", ans);
  return 0;
}