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;
mt19937_64 random_num(
    chrono::high_resolution_clock::now().time_since_epoch().count());
const int MOD = 1000000007;
const int base = 26;
const int arraysize = 100005;
int n;
struct point {
  long long x, y;
} a[305];
long long res;
long long area(point a, point b, point c) {
  return (b.x - a.x) * (a.y + b.y) + (c.x - b.x) * (b.y + c.y) +
         (a.x - c.x) * (c.y + a.y);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i].x >> a[i].y;
  for (int i = 1; i <= n; i++)
    for (int j = i + 1; j <= n; j++) {
      long long mn = 1e18, mx = -1e18;
      for (int k = 1; k <= n; k++)
        if (k != i && k != j) {
          long long s = area(a[i], a[j], a[k]);
          if (s == 0) continue;
          if (s < 0)
            mn = min(mn, s);
          else
            mx = max(mx, s);
        }
      if (mn != 0 && mx != 0) res = max(res, mx - mn);
    }
  if (res % 2)
    cout << res / 2 << ".5";
  else
    cout << res / 2;
}