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;
int chh;
const int N = 305, INF = ~0U >> 2;
int n;
int x[N], y[N];
int cs(int i, int j, int k) {
  return (x[j] - x[i]) * (y[k] - y[i]) - (x[k] - x[i]) * (y[j] - y[i]);
}
int main() {
  int ans, max0, max1, tmp;
  while (~scanf("%d", &n)) {
    for (int i = 0; i < (n); i++) scanf("%d %d", &x[i], &y[i]);
    ans = 0.0;
    for (int i = (0); i <= (n - 1); i++)
      for (int j = (i + 1); j <= (n - 1); j++) {
        max0 = max1 = -INF;
        for (int k = (0); k <= (n - 1); k++) {
          if (k == i || k == j) continue;
          tmp = cs(i, j, k);
          if (tmp > 0) {
            max0 = max(max0, tmp);
          } else {
            max1 = max(max1, -tmp);
          }
        }
        ans = max(ans, max0 + max1);
      }
    printf("%.6lf\n", ans / 2.0);
  }
  return 0;
}