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 = 10000010;
const int mod = 1000000007;
int n, x[305], y[305];
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d%d", &x[i], &y[i]);
  }
  int ans = 0, m1 = 0, m2 = 0;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      m1 = -maxn, m2 = -maxn;
      for (int k = 0; k < n; k++) {
        if (k != i && k != j) {
          int tmp =
              (x[j] - x[i]) * (y[k] - y[i]) - (x[k] - x[i]) * (y[j] - y[i]);
          if (tmp < 0)
            m1 = max(m1, -tmp);
          else
            m2 = max(m2, tmp);
        }
      }
      ans = max(ans, m1 + m2);
    }
  }
  printf("%.6lf\n", ans / 2.0);
  return 0;
}