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;
double x[500];
double y[500];
double s[500];
int main() {
  int a;
  scanf("%d", &a);
  for (int i = 0; i < a; i++) {
    scanf("%lf%lf", x + i, y + i);
  }
  double ret = 0;
  for (int i = 0; i < a; i++) {
    for (int j = i + 1; j < a; j++) {
      int N = 0;
      for (int k = 0; k < a; k++) {
        if (k == i) continue;
        if (k == j) continue;
        s[N++] = (x[k] - x[i]) * (y[j] - y[i]) - (x[j] - x[i]) * (y[k] - y[i]);
      }
      std::sort(s, s + a - 2);
      ret = max(ret, s[a - 3] - s[0]);
    }
  }
  printf("%.12f\n", ret / 2);
}