In-circles Again

The figure below shows triangle $ABC$ together with its in-circle (the circle that touches all three sides of the triangle from the inside). The radius of this in-circle is $r$. Three more circles are drawn; each of them touches two sides of the triangle and the in-circle of $ABC$. The radii of these three circles are $r_1$, $r_2$, and $r_3$.

Given the values of $r$, $r_1$, $r_2$, and $r_3$, find the area of triangle $ABC$.

The input consists of up to $1000$ datasets. Each dataset holds four positive floating-point numbers $r$, $r_1$, $r_2$, and $r_3$ in that order. The input is terminated by a dataset of four negative numbers.

The values are separated by whitespace (including newlines), so a single dataset may span several physical lines. Read the values as whitespace-separated tokens rather than line by line.

For each dataset print one line in the format Case k: A, where $k$ is the $1$-based dataset number and $A$ is the area of triangle $ABC$ shown to two digits after the decimal point. You may assume that a triangle $ABC$ can always be constructed from the given $r$, $r_1$, $r_2$, $r_3$. If needed you may take $\pi = 3.141592653589793$ and use double-precision floating-point numbers. No input is given for which small precision errors would change the printed output. Refer to the sample output for the exact format.