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;
inline int area(int x1, int y1, int x2, int y2, int x3, int y3) {
  int ax = x1 - x2, ay = y1 - y2;
  int bx = x1 - x3, by = y1 - y3;
  return ax * by - ay * bx;
}
int n, px[500], py[500];
int main() {
  while (scanf("%d", &n) == 1) {
    for (int i = 0; i < n; ++i) {
      scanf("%d%d", px + i, py + i);
    }
    double ans = 0;
    for (int i = 0; i < n; ++i) {
      for (int j = i + 1; j < n; ++j) {
        int ns = 0x7ffffff, ps = -ns;
        for (int k = 0; k < n; ++k) {
          if (k == i || k == j) continue;
          int t = area(px[i], py[i], px[j], py[j], px[k], py[k]);
          if (t < ns) ns = t;
          if (t > ps) ps = t;
        }
        if (ans < ps - ns) ans = ps - ns;
      }
    }
    printf("%lf\n", ans / 2);
  }
  return 0;
}