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 long long INF = (long long)1e18;
const long long MOD = (long long)1e9 + 9;
ifstream Cin("input.txt");
ofstream Cout("output.txt");
struct pt {
  int x, y;
};
int main() {
  int n, i, j, k, ll, rr, s, ans = 0;
  cin >> n;
  vector<pt> r(n);
  for (i = 0; i < n; ++i) cin >> r[i].x >> r[i].y;
  for (i = 0; i < n; ++i)
    for (j = 0; j < n; ++j)
      if (j != i) {
        ll = rr = 0;
        for (k = 0; k < n; ++k)
          if (k != i && k != j) {
            s = (r[j].x - r[i].x) * (r[k].y - r[i].y) -
                (r[j].y - r[i].y) * (r[k].x - r[i].x);
            ll = min(ll, s);
            rr = max(rr, s);
          }
        if (ll && rr) ans = max(ans, rr - ll);
      }
  printf("%.10f", ans / 2.);
}