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>
inline int ccw(int ax, int ay, int bx, int by, int cx, int cy) {
  return (ax * (by - cy) + bx * (cy - ay) + cx * (ay - by));
}
int N;
int x[310];
int y[310];
int ans;
int main(void) {
  scanf("%d", &N);
  for (int i = 0; i < N; ++i) {
    scanf("%d%d", &x[i], &y[i]);
  }
  for (int i = 0; i < N; ++i) {
    for (int j = 0; j < N; ++j) {
      if (i == j) continue;
      int mn = 0;
      int mx = 0;
      for (int k = 0; k < N; ++k) {
        if (j == k || i == k) continue;
        int _ccw = ccw(x[i], y[i], x[j], y[j], x[k], y[k]);
        if (_ccw > mx) mx = _ccw;
        if (_ccw < mn) mn = _ccw;
      }
      if (mn >= 0 || mx <= 0) continue;
      if (mx - mn > ans) ans = mx - mn;
    }
  }
  printf("%.6lf\n", ans / 2.0);
  return 0;
}