Love Log
---- ---

Olivia, the arrow beetle, is on the ground near a log.
On the other side of the log is Oliver, the love of her
life.  She wants to get to him.  How far must she
travel?

Olivia and Oliver are on the ground, the log rests on
the ground, and Olivia must fly over the top of the log
to get to Oliver.  You can assume that the ground is
perfectly flat and the log is a perfect cylinder with
axis perpendicular to the line between Olivia and
Oliver.  The distance B from Olivia to the point where
the log touches the ground, the distance C from this
point to Oliver, and the diameter D of the log are
given.  Arrow beetles fly in perfectly straight lines
when they need to get to a point they can see, and
otherwise can fly right next to a curved surface.  You
can assume `right next to' means infinitesimally close
to.

Olivia or Oliver can be in the shadow of the log; i.e.,
B < D/2 or C < D/2 are possible.


Input
-----

Several test cases, each with one line containing B, C,
and D, in that order.  0 < B,C,D < 1000000.  Input ends
with a line containing three zeros.

You should use double precision floating point arithme-
tic to do input and computation, as input with 3 decimal
places can have up to 9 significant digits.


Output
------

For each test case, one line containing the length of
the shortest arrow beetle flying route from Olivia to
Oliver.  This length must have exactly 3 decimal places.


Sample Input
------ -----

10.0 10.0 20.0
 0.1  0.1 20.0
10.0 80.0 20.0
0 0 0


Sample Output
------ ------
 
51.416
62.632
108.195


File:	   lovelog.txt
Author:	   Bob Walton <walton@deas.harvard.edu>
Date:	   Sun Oct 20 22:44:48 EDT 2002

The authors have placed this file in the public domain;
they make no warranty and accept no liability for this
file.

RCS Info (may not be true date or author):

    $Author: walton $
    $Date: 2002/10/21 02:46:01 $
    $RCSfile: lovelog.txt,v $
    $Revision: 1.3 $