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;
struct point {
  int x, y;
} a[400];
double get_sqr(point p1, point p2, point p3) {
  return (p3.x - p1.x) * (p2.y - p1.y) - (p2.x - p1.x) * (p3.y - p1.y);
}
double abs_(double x) { return x > 0 ? x : -x; }
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i].x >> a[i].y;
  double max = -1;
  for (int i = 0; i < n; i++)
    for (int j = i; j < n; j++) {
      double cur_max1 = -1, cur_min1 = 1000000000;
      for (int k = 0; k < n; k++) {
        if (get_sqr(a[i], a[j], a[k]) > 0 &&
            abs_(get_sqr(a[i], a[j], a[k])) > cur_max1)
          cur_max1 = abs_(get_sqr(a[i], a[j], a[k]));
        if (get_sqr(a[i], a[j], a[k]) > 0 &&
            abs_(get_sqr(a[i], a[j], a[k])) < cur_min1)
          cur_min1 = abs_(get_sqr(a[i], a[j], a[k]));
      }
      double cur_max2 = -1, cur_min2 = 1000000000;
      for (int k = 0; k < n; k++) {
        if (get_sqr(a[i], a[j], a[k]) < 0 &&
            abs_(get_sqr(a[i], a[j], a[k])) > cur_max2)
          cur_max2 = abs_(get_sqr(a[i], a[j], a[k]));
        if (get_sqr(a[i], a[j], a[k]) < 0 &&
            abs_(get_sqr(a[i], a[j], a[k])) < cur_min2)
          cur_min2 = abs_(get_sqr(a[i], a[j], a[k]));
      }
      double sum = -1;
      if (cur_max1 < 0)
        sum = cur_max2 - cur_min2;
      else if (cur_max2 < 0)
        sum = cur_max2 - cur_min2;
      else
        sum = cur_max1 + cur_max2;
      if (sum > max) max = sum;
    }
  cout << fixed << setprecision(9) << max / 2 << endl;
}