Friends in Space
------- -- -----

The space colony Bad Light consists of a large cluster
of asteroids what orbits the sun Dim Wit.  The asteroids
would drift apart, but are held together by wires.
Conveniently the wires are not required to withstand
much force, and are also useful for transporting oneself
between asteroids.  The system of Dim Wit is inhabited
by the Zkpt, somewhat intelligent creatures we will not
describe here.

Two pairs of friends are moving to Bad Light and need to
find apartments on the asteroids.  Zkpts never share an
apartment and friends never live on the same asteroid.
One pair of friends is Ba and Da who want to live on
asteroids as close together as possible.  Another pair
of friends Gz and Tz want to live as far apart as
possible (don't ask).

As a real estate broker you need to help both pairs of
friends.  You have a list of asteroids with available
apartments and their coordinates relative to a reference
point.


Input
-----

For each test case, first a line that gives the test
case name.  Then a line of the form

	N

giving the number of asteroids N.  This is followed by N
asteroid location lines each of the form

	X Y Z
	
giving the coordinates (X,Y,Z) of one asteroid, relative
to the center of the Bad Light cluster.  All coordinates
are integers.

	-1000 <= X,Y,Z <= 1,000
	3 <= N <= 100

For identification purposes the asteroids are numbered
1, ..., N in the order that their location lines are
given.

Input terminates with an end of file.  The test case
name line is at most 80 characters.


Output
------

For each test case, first an exact copy of the test case
name line.  Then a second line of the form

	MIN a1 a2 d

where a1 and a2 are the identifiers of the two closest
asteroids and d is the distance between them.  Lastly
a third line of the the form

	MAX a1 a2 d

where a1 and a2 are the identifiers of the two asteroids
that are farthest apart and d is the distance between
them.

To make autojudging easier THE JUDGE REQUIRES THAT
a1 < a2 in both the MIN and MAX lines.

Distances must be accurate to one part in 10**5 (use
default floating point format which prints 6 digits of
precision).


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

-- SAMPLE 1 --
4
 0 0 0
15 0 0
25 0 0
30 0 0
-- SAMPLE 2 --
6
  0  0  0
-10 10 10
 30 10 20
 20 10 30
 30 30 10
 10 30 10


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

-- SAMPLE 1 --
MIN 3 4 5
MAX 1 4 30
-- SAMPLE 2 --
MIN 3 4 14.1421
MAX 2 5 44.7214


File:	   friends.txt
Author:	   Bob Walton <walton@seas.harvard.edu>
Date:	   Sun Oct  1 02:20:39 EDT 2017

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