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[300], y[300], i, n, z, a, b, c, q1, q2, j, q, p, inf = 1000000000;
double S, mx, res, ans = 0;
double area(int i, int j, int q) {
  double S = (x[j] - x[i]) * (y[q] - y[i]) - (x[q] - x[i]) * (y[j] - y[i]);
  return S;
}
int test(int x) {
  if (x > 0)
    return 1;
  else
    return -1;
}
int main() {
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d%d", &x[i], &y[i]);
  for (i = 0; i < n - 1; i++)
    for (j = i + 1; j < n; j++) {
      mx = -inf;
      a = y[i] - y[j];
      b = x[j] - x[i];
      c = -(a * x[i] + b * y[i]);
      for (q = 0; q < n; q++)
        if (q != i && q != j) {
          p = a * x[q] + b * y[q] + c;
          if (p == 0) continue;
          S = abs(area(i, j, q));
          if (S > mx) {
            q1 = q;
            mx = S;
            z = test(p);
          }
        }
      if (mx == -inf) continue;
      res = mx;
      mx = -inf;
      for (q = 0; q < n; q++)
        if (q != i && q != j && test(a * x[q] + b * y[q] + c) != z) {
          p = a * x[q] + b * y[q] + c;
          if (p == 0) continue;
          S = abs(area(i, j, q));
          if (S > mx) mx = S;
        }
      if (mx == -inf) continue;
      ans = max(ans, res + mx);
    }
  printf("%.9lf\n", ans / 2);
}