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;
const int dr[]{-1, -1, 0, 1, 1, 1, 0, -1};
const int dc[]{0, 1, 1, 1, 0, -1, -1, -1};
void run() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
}
typedef complex<double> point;
template <class T>
istream &operator>>(istream &is, complex<T> &p) {
  T value;
  is >> value;
  p.real(value);
  is >> value;
  p.imag(value);
  return is;
}
double triangleArea(double a, double b, double c) {
  double s = 0.5 * (a + b + c);
  return sqrt(s * (s - a) * (s - b) * (s - c));
}
double triangleArea(point p0, point p1, point p2) {
  double a = (hypot((((p0) - (p1))).imag(), (((p0) - (p1))).real())),
         b = (hypot((((p0) - (p2))).imag(), (((p0) - (p2))).real())),
         c = (hypot((((p1) - (p2))).imag(), (((p1) - (p2))).real()));
  return triangleArea(a, b, c);
}
int ccw(point a, point b, point c) {
  point v1(b - a), v2(c - a);
  int t = ((conj(v1) * (v2)).imag());
  if (t > 0) return 1;
  if (t < 0) return -1;
  if (v1.real() * v2.real() < 0 || v1.imag() * v2.imag() < 0) return -1;
  if (norm(v1) < norm(v2) - 1e-8) return 1;
  return 0;
}
int main() {
  run();
  int n;
  cin >> n;
  vector<point> v(n);
  for (auto &it : v) cin >> it;
  double res = 0;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      double maxUp = -1e-8, maxDown = -1e-8;
      for (int k = 0; k < n; k++) {
        if (k == i || k == j) continue;
        double area =
            ((conj(((v[i]) - (v[j]))) * (((v[i]) - (v[k])))).imag()) * 0.5;
        int dr = ccw(v[i], v[j], v[k]);
        if (dr < 0)
          maxUp = max(maxUp, -area);
        else if (dr > 0)
          maxDown = max(maxDown, area);
      }
      if (maxUp > 1e-8 && maxDown > 1e-8) res = max(res, maxUp + maxDown);
    }
  }
  cout << fixed << setprecision(9) << res;
}