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;
template <class T>
inline T GCD(T a, T b) {
  return b ? GCD(b, a % b) : a;
}
template <class T>
inline T LCM(T a, T b) {
  if (a < 0) return LCM(-a, b);
  if (b < 0) return LCM(a, -b);
  return a * (b / GCD(a, b));
}
void crossproduct(int x1, int y1, int x2, int y2, int &z) {
  z = x1 * y2 - y1 * x2;
}
long long int dotproduct(long long int z1, long long int z2) { return z1 * z2; }
int sameside(int x1, int y1, int x2, int y2, int x3, int y3, int x, int y) {
  int a, b;
  crossproduct(x2 - x1, y2 - y1, x3 - x1, y3 - y1, a);
  crossproduct(x2 - x1, y2 - y1, x - x1, y - y1, b);
  if (dotproduct(a, b) >= 0)
    return 1;
  else
    return 0;
}
int main() {
  int n, x, y, refx, refy, areamul2, finalarea, maxarea = 0;
  cin >> n;
  vector<pair<int, int> > p;
  vector<int> areamul2vec1, areamul2vec2;
  double maxarea1;
  for (long long int i = 0; i < n; i++) {
    cin >> x >> y;
    p.push_back(make_pair(x, y));
  }
  for (long long int i = 0; i < n; i++) {
    for (long long int j = i + 1; j < n; j++) {
      refx = p[i].first;
      refy = p[i].second + 1;
      for (long long int k = 0; k < n; k++) {
        if (k != j && k != i) {
          areamul2 = abs((p[j].first * p[i].second - p[i].first * p[j].second) +
                         (p[k].first * p[j].second - p[j].first * p[k].second) +
                         (p[i].first * p[k].second - p[k].first * p[i].second));
          if (sameside(p[i].first, p[i].second, p[j].first, p[j].second,
                       p[k].first, p[k].second, refx, refy)) {
            areamul2vec1.push_back(areamul2);
          } else {
            areamul2vec2.push_back(areamul2);
          }
        }
      }
      if (areamul2vec1.size() != 0 && areamul2vec2.size() != 0) {
        finalarea = *max_element(areamul2vec1.begin(), areamul2vec1.end()) +
                    *max_element(areamul2vec2.begin(), areamul2vec2.end());
        if (finalarea > maxarea) {
          maxarea = finalarea;
        }
      }
      areamul2vec1.clear();
      areamul2vec2.clear();
    }
  }
  maxarea1 = (maxarea * 1.0) / 2.0;
  printf("%lf\n", maxarea1);
  return 0;
}