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 int MAXN = 310;
const double eps = 1e-10;
struct Point {
  double x, y;
  Point(double x = 0, double y = 0) : x(x), y(y) {}
} p[MAXN], ch[MAXN];
int dcmp(double x) {
  if (fabs(x) < eps)
    return 0;
  else
    return x < 0 ? -1 : 1;
}
bool operator<(Point A, Point B) {
  return A.x < B.x || (A.x == B.x && A.y < B.y);
}
Point operator-(Point A, Point B) { return Point(A.x - B.x, A.y - B.y); }
bool operator==(Point A, Point B) {
  if (dcmp(A.x - B.x) == 0 && dcmp(A.y - B.y) == 0) return 1;
  return 0;
}
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 Cross(Point A, Point B) { return A.x * B.y - A.y * B.x; }
int ConvexHull(int n) {
  int m = 0, i;
  double d;
  for (i = 0; i < n; i++) {
    d = Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2]);
    while (m > 1 && dcmp(d) <= 0) {
      m--;
      d = Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2]);
    }
    ch[m++] = p[i];
  }
  int k = m;
  for (i = n - 2; i >= 0; i--) {
    d = Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2]);
    while (m > k && dcmp(d) <= 0) {
      m--;
      d = Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2]);
    }
    ch[m++] = p[i];
  }
  if (n > 1) m--;
  return m;
}
double Area(double l1, double l2, double l3) {
  double l = (l1 + l2 + l3) * 0.5;
  return sqrt(l * (l - l1) * (l - l2) * (l - l3));
}
int main() {
  int n, i, cnt, j, k, l;
  double ans, area;
  Point v1, v2, v3, v4, v5;
  while (scanf("%d", &n) != EOF) {
    for (i = 0; i < n; i++) scanf("%lf%lf", &p[i].x, &p[i].y);
    sort(p, p + n);
    cnt = ConvexHull(n);
    ans = 0.0;
    if (cnt > 3) {
      for (i = 0; i < cnt; i++) {
        for (j = i + 1; j < cnt; j++) {
          for (k = j + 1; k < cnt; k++) {
            for (l = k + 1; l < cnt; l++) {
              v1 = ch[i] - ch[j];
              v2 = ch[j] - ch[k];
              v3 = ch[k] - ch[l];
              v4 = ch[l] - ch[i];
              v5 = ch[j] - ch[l];
              area = Area(Length(v1), Length(v4), Length(v5)) +
                     Area(Length(v2), Length(v3), Length(v5));
              if (dcmp(ans - area) < 0) ans = area;
            }
          }
        }
      }
    } else {
      v1 = ch[0] - ch[1];
      v2 = ch[1] - ch[2];
      v5 = ch[0] - ch[2];
      for (i = 0; i < n; i++) {
        if (!(p[i] == ch[0]) && !(p[i] == ch[1]) && !(p[i] == ch[2])) {
          v3 = ch[2] - p[i];
          v4 = p[i] - ch[0];
          area = Area(Length(v1), Length(v2), Length(v5)) -
                 Area(Length(v4), Length(v3), Length(v5));
          if (dcmp(ans - area) < 0) ans = area;
        }
      }
    }
    printf("%.9f\n", ans);
  }
  return 0;
}