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 n;
double x[500], y[500], ans = 0;
double cross(int i, int j) { return x[i] * y[j] - y[i] * x[j]; }
double area(int i, int j, int k) {
  return cross(i, j) + cross(j, k) + cross(k, i);
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    std::cin >> x[i] >> y[i];
  }
  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j <= n; ++j) {
      double max = -1e9, min = 1e9;
      for (int k = 1; k <= n; ++k) {
        if (k == i || k == j) continue;
        max = std::max(max, area(i, j, k));
        min = std::min(min, area(i, j, k));
      }
      ans = std::max(ans, max - min);
    }
  }
  printf("%.10f", ans / 2);
  return 0;
}