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;
int n, kq;
pair<int, int> a[305];
int CCW(int x, int y, int z) {
  int tong = 0;
  tong += (a[y].first - a[x].first) * (a[y].second + a[x].second);
  tong += (a[z].first - a[y].first) * (a[z].second + a[y].second);
  tong += (a[x].first - a[z].first) * (a[x].second + a[z].second);
  return tong;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i].first >> a[i].second;
  for (int i = 1; i <= n - 1; i++)
    for (int j = i + 1; j <= n; j++) {
      int res = -1000000000, res1 = -1000000000;
      for (int t = 1; t <= n; t++)
        if (CCW(i, j, t) < 0) res = max(res, -CCW(i, j, t));
      for (int t = 1; t <= n; t++)
        if (CCW(i, j, t) > 0) res1 = max(res1, CCW(i, j, t));
      kq = max(kq, res + res1);
    }
  cout << kq / 2;
  if (kq % 2 == 1) cout << ".5";
}