Maximal Area Quadrilateral

1000ms

262144K

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.

Input:

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 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.

Sample Input:

Sample 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.

Informação

Provedor Codeforces

Código CF340B