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;
const double eps = 1e-9;
struct Point {
  double x, y;
  Point(double x = 0, double y = 0) : x(x), y(y) {}
} coordinate[350];
Point operator+(Point A, Point B) { return Point(A.x + B.x, A.y + B.y); }
Point operator-(Point A, Point B) { return Point(A.x - B.x, A.y - B.y); }
Point operator*(Point A, double p) { return Point(A.x * p, A.y * p); }
Point operator/(Point A, double p) { return Point(A.x / p, A.y / p); }
int dcmp(double x) {
  if (fabs(x) < eps) return 0;
  return x < 0 ? -1 : 1;
}
double Dot(Point A, Point B) { return A.x * B.x + A.y * B.y; }
double Length(Point A) { return sqrt(Dot(A, A)); }
double Angle(Point A, Point B) {
  return acos(Dot(A, B) / Length(A) / Length(B));
}
double Cross(Point A, Point B) { return A.x * B.y - A.y * B.x; }
double Area(Point A, Point B, Point C) { return Cross(B - A, C - A) / 2.0; }
int main(int argc, char const *argv[]) {
  int n;
  while (cin >> n) {
    double res = 0.0;
    for (int i = 0; i < n; i++) {
      cin >> coordinate[i].x >> coordinate[i].y;
    }
    for (int i = 0; i < n; i++) {
      for (int j = i + 1; j < n; j++) {
        double up = 0.0, down = 0.0;
        for (int k = 0; k < n; k++) {
          if (k == i || k == j) continue;
          double area = Area(coordinate[i], coordinate[j], coordinate[k]);
          if (dcmp(area) > 0)
            up = max(up, area);
          else
            down = max(down, -area);
        }
        if (dcmp(up) && dcmp(down)) res = max(res, up + down);
      }
    }
    printf("%lf\n", res);
  }
  return 0;
}