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;
} g[500];
int main() {
  int i, j, k, n, m;
  scanf("%d", &n);
  for (i = 0; i < n; ++i) {
    scanf("%lf%lf", &g[i].x, &g[i].y);
  }
  double maxx = 0;
  double m1, m2;
  for (i = 0; i < n - 1; ++i)
    for (j = i + 1; j < n; ++j) {
      m1 = m2 = 0;
      for (k = 0; k < n; ++k) {
        if (i == k || j == k) continue;
        double temp = (g[i].x - g[k].x) * (g[j].y - g[k].y) -
                      (g[j].x - g[k].x) * (g[i].y - g[k].y);
        if (temp > 0) {
          if (temp > m1) m1 = temp;
        } else {
          if (temp < m2) m2 = temp;
        }
      }
      if (m1 != 0 && m2 != 0)
        if (maxx < m1 + abs(m2)) maxx = m1 + abs(m2);
    }
  printf("%lf", maxx / 2);
}