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>
int dx[] = {0, -1, 0, 1, -1, 1, -1, 1};
int dy[] = {-1, 0, 1, 0, 1, -1, -1, 1};
const int N = 2e5 + 5, oo = 1e9;
const long long MOD = 1e9 + 7, MOD2 = 1e9 + 9, p1 = 1000003, p2 = 1000033;
const double pi = acos(-1);
using namespace std;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  complex<long double> arr[n + 5];
  for (int i = 0; i < n; i++) {
    long double x, y;
    cin >> x >> y;
    arr[i] = complex<long double>(x, y);
  }
  long double ans = 0;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      long double pos = 0, neg = 0;
      for (int k = 0; k < n; k++) {
        if (k != i and k != j) {
          long double area =
              ((conj(((arr[j]) - (arr[i]))) * (((arr[k]) - (arr[i])))).imag());
          if (area > 0)
            pos = max(pos, area / 2.0);
          else
            neg = min(neg, area / 2.0);
        }
      }
      if (pos > 0 and neg < 0) ans = max(ans, pos + (-neg));
    }
  }
  cout << fixed << setprecision(9) << ans;
  return 0;
}