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;
pair<int, int> first[301];
inline double ccw(pair<int, int> A, pair<int, int> B, pair<int, int> C) {
  return ((double)(B.first - A.first) * (C.second - B.second) -
          (B.second - A.second) * (C.first - B.first)) *
         0.5;
}
inline double chmax(double &A, double B) {
  if (B - A > 0.00000001) A = B;
}
int main() {
  int n;
  double maxArea = 0;
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d%d", &first[i].first, &first[i].second);
  for (int i = 1; i <= n; ++i)
    for (int j = i + 1; j <= n; ++j) {
      double maxMinus = -1, maxPlus = -1;
      for (int k = 1; k <= n; ++k)
        if (k != i && k != j)
          if (ccw(first[i], first[j], first[k]) < 0)
            chmax(maxMinus, -ccw(first[i], first[j], first[k]));
          else
            chmax(maxPlus, ccw(first[i], first[j], first[k]));
      if (maxPlus >= 0 && maxMinus >= 0) chmax(maxArea, maxMinus + maxPlus);
    }
  printf("%lf", maxArea);
  return 0;
}