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;
} p[301];
int cross(struct Point A, struct Point B, struct Point c);
double area(struct Point A, struct Point B, struct Point c);
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> p[i].x >> p[i].y;
  }
  double ar = 0;
  for (int i = 0; i < n; i++)
    for (int j = i + 1; j < n; j++) {
      int m1, m2;
      double a1, a2;
      a1 = a2 = 0;
      m1 = m2 = -1;
      for (int k = 0; k < n; k++) {
        if (k == i || k == j) continue;
        int t = cross(p[i], p[j], p[k]);
        double dd = area(p[i], p[j], p[k]);
        if (t) {
          if (dd > a1) {
            a1 = dd;
            m1 = k;
          }
        } else {
          if (dd > a2) {
            a2 = dd;
            m2 = k;
          }
        }
      }
      if (m1 >= 0 && m2 >= 0) ar = max(ar, a1 + a2);
    }
  cout.precision(10);
  cout << ar << endl;
  return 0;
}
int cross(struct Point A, struct Point B, struct Point C) {
  int v1[2], v2[2];
  v1[0] = B.x - A.x;
  v1[1] = B.y - A.y;
  v2[0] = C.x - A.x;
  v2[1] = C.y - A.y;
  return (v1[0] * v2[1] - v1[1] * v2[0] > 0);
}
double area(struct Point A, struct Point B, struct Point C) {
  double area = 0;
  area += (B.x * A.y - B.y * A.x);
  area += (C.x * B.y - C.y * B.x);
  area += (A.x * C.y - A.y * C.x);
  area *= 0.5;
  if (area < 0) area = -area;
  return area;
}