3344: Maximal Area Quadrilateral
Description
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: 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 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.
5
0 0
0 4
4 0
4 4
2 3
16.000000
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.