Stained Carpet

The Algebraist Carpet Manufacturing (ACM) group makes area carpets from geometric figures. The 2014 ACM carpets are all equilateral triangles. A manufacturing defect left some of them less stain resistant than intended, so the ACM group replaces every carpet that has a stain on it.

The web form that reports a stained carpet asks for the three distances from the stain to the corners of the rug. From those three numbers, compute the area of the rug to send to the customer, or report that the carpet did not come from ACM.

The stain is a point of the plane the carpet lies in. Several equilateral carpets can have their three corners at distances $a$, $b$ and $c$ from one point, and in that case you report the area of the largest one.

The input is a single test case. One line holds three floating point numbers $a$, $b$ and $c$ ($0 < a, b, c \le 100$), the distances from the stain to each of the three corners. One space separates $a$ and $b$, and one space separates $b$ and $c$.

Print a single line with a single floating point number. If some equilateral carpet has its three corners at distances $a$, $b$ and $c$ from a point of its plane, print the area of the largest such carpet. Otherwise print -1.000. Print the number rounded to exactly three decimal places, with no spaces.