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;
string toStr(long long n) {
  stringstream ss;
  ss << n;
  return ss.str();
}
int toNum(string s) {
  stringstream ss;
  long long n;
  ss << s;
  ss >> n;
  return n;
}
int main() {
  int n;
  cin >> n;
  int x[n], y[n];
  for (int i = 0; i < n; i++) cin >> x[i] >> y[i];
  int ans = 0;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      int ax = x[i] - x[j];
      int ay = y[i] - y[j];
      int a1 = -1e9;
      int a2 = 1e9;
      for (int k = 0; k < n; k++) {
        if (k != i && k != j) {
          int bx = x[k] - x[j];
          int by = y[k] - y[j];
          int pv = ax * by - bx * ay;
          if (pv >= 0) a1 = max(a1, pv);
          if (pv <= 0) a2 = min(a2, pv);
        }
        ans = max(ans, a1 - a2);
      }
    }
  }
  cout.precision(9);
  cout << (double)ans / 2;
  return 0;
}