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;
const int MAXN = 200000;
const double INF = 1000.0 * 1000 * 1000;
struct Point {
  double x, y;
};
Point a[MAXN];
double pos, max1, min2;
int n;
double vect(int i, int j, int k) {
  return (a[j].x - a[i].x) * (a[k].y - a[i].y) -
         (a[k].x - a[i].x) * (a[j].y - a[i].y);
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i].x >> a[i].y;
  for (int i = 1; i <= n; i++)
    for (int j = i + 1; j <= n; j++) {
      max1 = -INF;
      min2 = INF;
      for (int k = 1; k <= n; k++) {
        if (k == i || k == j) continue;
        if (vect(i, j, k) > 0)
          max1 = max(max1, vect(i, j, k) / 2);
        else
          min2 = min(min2, vect(i, j, k) / 2);
      }
      pos = max(pos, max1 - min2);
    }
  printf("%.14lf", pos);
  return 0;
}