A9089. Maximal Area Quadrilateral

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.

The first line contains integer $n$ ( $4<=n<=300$ ). Each of the next $n$ lines contains two integers: $x_{i}$ , $y_{i}$ $(-1000<=x_{i},y_{i}<=1000)$ — the cartesian coordinates of $i$ th special point. It is guaranteed that no three points are on the same line. It is guaranteed that no two points coincide.

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 $10^{-9}$ .

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 $4·4=16$ .