Find the Perimeter

If there is a point P inside or outside a triangle ABC, so that three triangles ABP, ACP, and BCP have equal perimeters, we say P is the perimeter center of triangle ABC, the perimeter of ABP, ACP and BCP is denoted by Q(ABC).


For example, in an equilateral triangle with each side 10 in figure 1, the P at its center satisfies the above condition and Q(ABC)=21.54701 (=10+20/sqrt(3)).

Input contains several cases. Each case has one line containing three integers a, b, c, indicating the lengths of the respective sides of a triangle. Note that 0 < a, b, c ≤ 100. The input is terminated by three zeros.

For each case, you should output the Q(ABC) to five decimal places, if there is a triangle whose side lengths are a, b, c, with a unique perimeter center. Otherwise, output a single -1.

10 10 10
30 40 50
18 17 15
1 2 3
0 0 0

21.54701
120.00000
36.54972
-1

2006 Asia Regional Xi-An （Preliminary）