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;
complex<double> p[300];
void read();
void solve();
inline double cross(complex<double> u, complex<double> v) {
  return imag(conj(u) * v);
}
int main() {
  read();
  solve();
  return 0;
}
void read() {
  double x, y;
  cin >> N;
  for (int i = 0; i < N; ++i) cin >> x >> y, p[i] = complex<double>(x, y);
}
void solve() {
  double res = 0.0;
  for (int i = 0; i < N; ++i)
    for (int j = i + 1; j < N; ++j) {
      double mx = 0.0, mn = 0.0;
      for (int k = 0; k < N; ++k)
        if (k != i && k != j) {
          mx = max(mx, cross(p[j] - p[i], p[k] - p[i]));
          mn = min(mn, cross(p[j] - p[i], p[k] - p[i]));
        }
      if (mx != 0.0 && mn != 0.0) res = max(res, mx + abs(mn));
    }
  cout.setf(ios::fixed), cout.precision(10);
  cout << (0.5 * res) << "\n";
}