3D Convex Hull
-- ------ ----

You are given a large number of points in 3-space and
must find the convex hull of these points.


Input
-----

For each test case, one line containing the name of the
test case, followed by a line containing just `n', the
number of points you are given, followed by n lines each
containing `x y z', the coordinates of one of the
points.  The points are numbered 1 through n in the
order that they appear in the input file.

The xyz coordinates are all integers in the range from
-1000 through +1000.  4 <= n <= 10,000.

The input ends with an end of file.


Output
------

For each test case, one line containing just the name
of the test case, followed by a line containing just
`m', the number of edges in the convex hull, followed by
m lines, each containing `i j', where i and j are the
numbers of the points that are the vertices of one of
these edges.  The input will be such that 4 <= m <= 100.
An edge, by definition, is the edge of a face of the
convex hull, and such a face can be any convex polygon.

To simplify the code, the input will be such that each
face is a triangle and all points on the convex hull
will be vertices of faces.  Thus no point will be in the
interior of a face or on the line between two other
points that are on the hull.

All the hull face edges must be output in SORTED order.
For an edge output as `i j', i < j is required.  Edges
with lower i values must be output first, and among
edges with the same i values, those with lower j values
must be output first.


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

TETRAHEDRON IN A CUBE
4
0 0 0
1 1 0
0 1 1
1 0 1
OCTAHEDRON
9
0 0 0
2 0 0
0 2 0
2 2 0
1 1 -2
1 1 2
1 1 -1
1 1 0
1 1 1

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

TETRAHEDRON IN A CUBE
6
1 2
1 3
1 4
2 3
2 4
3 4
OCTAHEDRON
12
1 2
1 3
1 5
1 6
2 4
2 5
2 6
3 4
3 5
3 6
4 5
4 6


File:	   convexhull.txt
Author:	   Bob Walton <walton@deas.harvard.edu>
Date:	   Wed Oct 15 09:30:27 EDT 2008

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: 2008/10/15 13:31:45 $
    $RCSfile: convexhull.txt,v $
    $Revision: 1.7 $