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 point {
  double x, y;
};
double Direction(point pi, point pj, point pk) {
  return (pj.x - pi.x) * (pk.y - pi.y) - (pk.x - pi.x) * (pj.y - pi.y);
}
int main() {
  int n;
  point data[350];
  while (cin >> n) {
    for (int i = 0; i < n; i++) scanf("%lf%lf", &data[i].x, &data[i].y);
    double ans = 0;
    for (int i = 0; i < n; i++)
      for (int j = i + 1; j < n; j++) {
        double ma = -1e10, mi = 1e10;
        for (int k = 0; k < n; k++)
          if (k != i && k != j) {
            double o = Direction(data[i], data[j], data[k]);
            if (o < 0)
              mi = min(mi, o);
            else
              ma = max(ma, o);
          }
        if (ma > 0 && mi < 0) ans = max(ans, ma - mi);
      }
    printf("%.10f\n", ans / 2);
  }
  return 0;
}