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;
vector<pair<int, int> > points;
int n;
double result = -1;
inline double get_abs(double first) { return first > 0 ? first : -first; }
inline bool CCW(pair<int, int> a, pair<int, int> b, pair<int, int> c) {
  int sign = a.first * b.second + b.first * c.second + c.first * a.second;
  sign -= (b.first * a.second + c.first * b.second + a.first * c.second);
  return sign > 0;
}
inline double get_area(pair<int, int> a, pair<int, int> b, pair<int, int> c) {
  double area = a.first * b.second + b.first * c.second + c.first * a.second;
  area -= (b.first * a.second + c.first * b.second + a.first * c.second);
  return abs(area) / 2.0;
}
void get_max_min(double& maxmax, double& minmin, vector<pair<int, int> > p,
                 int inx1, int inx2) {
  for (int i = 0; i < p.size(); i++) {
    double myvalue = get_area(p[i], points[inx1], points[inx2]);
    maxmax = max(myvalue, maxmax);
    minmin = min(myvalue, minmin);
  }
}
void get_result(int inx1, int inx2) {
  vector<pair<int, int> > above;
  vector<pair<int, int> > below;
  double above_max = -1, above_min = 987987987, below_max = -1,
         below_min = 987987987;
  for (int i = 0; i < points.size(); i++) {
    if (i == inx1 || i == inx2) continue;
    if (CCW(points[inx1], points[inx2], points[i]) == true)
      above.push_back(points[i]);
    else
      below.push_back(points[i]);
  }
  if (above.size() == 0 || below.size() == 0) return;
  get_max_min(above_max, above_min, above, inx1, inx2);
  get_max_min(below_max, below_min, below, inx1, inx2);
  result = max(result, above_max + below_max);
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    int a, b;
    scanf("%d %d", &a, &b);
    points.push_back(make_pair(a, b));
  }
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      get_result(i, j);
    }
  }
  printf("%lf\n", result);
  return 0;
  return 0;
  return 0;
}