Bubblegram
----------

Iffy the `artist' produces a kind of abstract painting
that he calls a `bubblegram'.  This consists of a bunch
of non-intersecting circles that Iffy paints different
colors.  To help him, Iffy has built a machine that will
project a random circle on the canvas.  He can then
accept or reject the circle.

However, many of his bubblegrams have so many circles
that Iffy has trouble seeing if the projected circle
intersects any existing circle.  So he wants you to
build a second machine that tells him if a projected
circle intersects an existing circle.

More specifically, he wants your machine to output the
FIRST one of the following `judgments' that applies:

    inside	The projected circle is inside some
		existing circle, OR, some existing
		circle is inside the projected circle.
    overlap	The projected circle partly overlaps an
    		existing circle (the intersection has
		non-zero area less than the area of
		either circle).
    touch	The projected circle just touches an
    		existing circle.
    outside	The projected circle is completely
    		outside all existing circles.

As a first cut, you are to write a program that works
if there is only one existing circle.


Input
-----

A sequence of test cases.  Each test case consists of
a single line of the form:

	XP YP RP XE YE RE

defining a projected circle with center (XP,YP) and
radius RP and an existing circle of center (XE,YE) and
radius RE.

	-1,000 <= XP,YP,XE,YE <= +1,000
	1 <= RP,RE <= 500

All numbers are integers.  Input ends with an end of
file.


Output
------

For each test case, one line, consisting of a copy of
the test case input line followed by space character
followed by the judgment.

NOTE: Because input numbers are integers, you can solve
      this problem without using floating point arith-
      metic in a way that makes the judgments precise.
      The judge's solution does this.  It is still
      possible to solve the problem using floating point
      if you treat tiny values as equal to zero.


Display
-------

The input can be displayed in X-Windows or printed by
the commands

	display_bubbles sample.in
	display_bubbles sample.test
	print_bubbles sample.in
	print_bubbles sample.test

where the .in or .test files can be replaced by any test
case input or output file.


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

0 0 5 0 0 4
0 0 5 1 0 4
0 0 5 1 0 6
0 0 5 8 0 4
0 0 5 8 0 3
0 0 5 9 0 3
-3 10 10 1 13 15
-3 10 10 1 13 5
-3 10 10 1 13 6
-3 10 10 9 19 6
-3 10 10 9 19 5
-3 10 10 9 19 4


Sample Output
------ ------

0 0 5 0 0 4 inside
0 0 5 1 0 4 inside
0 0 5 1 0 6 inside
0 0 5 8 0 4 overlap
0 0 5 8 0 3 touch
0 0 5 9 0 3 outside
-3 10 10 1 13 15 inside
-3 10 10 1 13 5 inside
-3 10 10 1 13 6 overlap
-3 10 10 9 19 6 overlap
-3 10 10 9 19 5 touch
-3 10 10 9 19 4 outside


File:	   	bubblegram.txt
Author:	   	Bob Walton <walton@seas.harvard.edu>
Contributor:	Shai Simonson <shai@stonehill.edu>
Date:	   	Tue Oct 15 14:00:26 EDT 2019

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