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 x[100001], y[100001];
int ddd(int a, int b, int c) {
  return (x[a] - x[c]) * (y[b] - y[c]) - (x[b] - x[c]) * (y[a] - y[c]);
}
int main() {
  int n, a, b, c, s = 0, w;
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> x[i] >> y[i];
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++)
      if (i != j) {
        a = b = -INT_MAX;
        for (int k = 1; k <= n; k++)
          if (k != i && k != j) {
            w = ddd(k, j, i);
            if (w <= 0) a = max(a, abs(w));
            if (w >= 0) b = max(b, abs(w));
          }
        s = max(s, a + b);
      }
  cout.precision(12);
  cout << (double)s / 2;
}