Minimum Wrapping Material Area

FaQiang Company produces a metal product made up of several straight metal bars that are welded together at their intersections. For aesthetic reasons, the product is covered with a special wrapping material. In order to reduce costs, the company wants to use the minimum amount of material possible (ignoring scraps from cutting). This is equivalent to wrapping the product in the smallest possible area that fully covers it. Given the coordinates of the vertices of the product, your task is to compute the minimum area of material required. The wrapping area corresponds to the area of the convex hull of the given points. The answer should be output rounded to six decimal places (using standard rounding rules).

inputFormat

The input begins with an integer n (n ≥ 1), representing the number of vertices. The following n lines each contain two space-separated real numbers, representing the x and y coordinates of a vertex.

outputFormat

Print a single number — the area of the convex hull of the given points, rounded to six decimal places. The answer must be output in LaTeX formatted precision as follows: \(area = 1.000000\) (example).

sample

4
0 0
0 1
1 1
1 0

1.000000