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> a[309];
int n;
pair<int, int> operator-(pair<int, int> a, pair<int, int> b) {
  return make_pair(a.first - b.first, a.second - b.second);
}
int operator*(pair<int, int> a, pair<int, int> b) {
  return a.first * b.second - a.second * b.first;
}
int ccw(pair<int, int> a, pair<int, int> b, pair<int, int> c) {
  return (a - b) * (a - c);
}
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;
  }
  int res = 0;
  for (int i = 1; i <= n; ++i)
    for (int j = i + 1; j <= n; ++j) {
      int mx = -1e9, mn = 1e9;
      for (int t = 1; t <= n; ++t)
        if (t != j && t != i) {
          int s = ccw(a[i], a[j], a[t]);
          mx = max(mx, s);
          mn = min(mn, s);
        }
      res = max(res, mx - mn);
    }
  cout << fixed << setprecision(2) << res / 2.0;
  return 0;
}