Fair Eye's Secret
-----------------

Fair Eye, the referee, is known for making correct
calls. Scooper, the news reporter, thinks he has figured
out the secret of Fair Eye's success.  Just before
making a call, Fair Eye carefully positions himself
at an equal distance from any place where an event that
needs to be called may occur.

To test his theory Scooper uses Sky Cam to measure the
location F of Fair Eye and the locations P1, P2, P3 of
places where events that may need to be called occur.
For some reason there are almost always three such
places, and Scooper ignores the cases where there are
not three.  To test his theory Scooper wants to compute
for every three places P1, P2, and P3 the exact location
of the point C equidistant from these three places, so
that C may be compared to F, where Fair Eye positions
himself.

Mathematicians call C the circumcenter of P1, P2, and
P3, or of the triangle whose vertices are P1, P2, and
P3.  It is the center of the circumscribed circle of
that triangle.


Input
-----

For each case, a single line containing the 6 numbers

	x1 y1 x2 y2 x3 y3

defining three points: P1 = (x1,y1), P2 = (x2,y2), and
P3 = (x3,y3).  The 6 numbers are real numbers (and may
be negative).

An end of file terminates the input.


Output
------

For each case, a single line containing the 2 numbers

	x y

defining the circumcenter C = (x,y) of the three points
P1, P2, P3.

Both x and y must be printed with exactly 3 decimal
places.

You may assume that double precision floating point
numbers will suffice to compute C with adequate
precision, and that the three points are not so close
to being co-linear that there will be computation
problems.


Example Input
------- -----

0.0 0.0 1.0 0.0 0.0 1.0
0.0 0.0 1.0 1.0 0.0 1.0
0.0 0.0 1.0 2.0 2.0 0.0

Example Output
------- ------

0.500 0.500
0.500 0.500
1.000 0.750


File:	   faireye.txt
Author:	   Bob Walton <walton@deas.harvard.edu>
Date:	   Tue Oct 18 11:29:13 EDT 2005

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: 2005/10/18 15:30:23 $
    $RCSfile: faireye.txt,v $
    $Revision: 1.4 $