Nested Crates
------ ------

Given the length, width, and depth of each of a set of
crates, determine the maximum number that can be nested
inside each other.  Because the foam used to pack crates
inside each other consists of rectilinear blocks, a
nested crate must have sides parallel to its containing
crate.  Thus a crate fits in another if and only each
dimension of the smaller is less than the corresponding
dimension of the larger (where crates can be rotated, of
course).


Input
-----

For each of several test cases, first one line con-
taining just the test case name, and then one line
containing just the number N of crates, and then
N lines each containing

	H W D

where H, W, and D are the height, width, and depth
of one crate.  All numbers are integers.  Some of
the crates are very small and some very large; a
bit strange, but true.

	2 <= N <= 100
	1 <= H,W,D <= 1,000

Input ends with an end of file.


Output
------

For each test case, first a copy of the test case name
line from the input, and then one line containing just
the maximum number of crates that can be nested inside
each other.  Note that the largest crate in a set of
nested crates is counted, so if no two crates nest, the
answer is `1'.


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

-- SAMPLE 1 --
2
1 1 1
4 6 1
-- SAMPLE 2 --
4
1 1 1
2 2 2
3 3 3
1 2 3
-- SAMPLE 3 --
5
2 2 2
3 3 3
4 4 4
2 2 3
1 1 2

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

-- SAMPLE 1 --
1
-- SAMPLE 2 --
3
-- SAMPLE 3 --
3


Tips
----

Input consists of lines read from the standard input.
Input ends when an end-of-file is read from the standard
input.  Output consists of lines written to the standard
output.  For example input/output code see

    ~/demos/solutions/summer/summer.EXT

where EXT is c, cc, or java.

You can add debugging code that prints which crates
can be nested inside which other crates.  The output
of running `make debug' on the judge's solution is:

-- SAMPLE 1 --
(1,1,1)
1
-- SAMPLE 2 --
(1,1,1)<(2,2,2)
(1,1,1)<(3,3,3)
(2,2,2)<(3,3,3)
(1,1,1)<(2,2,2)<(3,3,3)
3
-- SAMPLE 3 --
(2,2,2)<(3,3,3)
(2,2,2)<(4,4,4)
(3,3,3)<(4,4,4)
(2,2,3)<(4,4,4)
(1,1,2)<(3,3,3)
(1,1,2)<(4,4,4)
(1,1,2)<(2,2,3)
(1,1,2)<(3,3,3)<(4,4,4)
3

Here the judge, being a bit of a debugging fanatic, has
taken the trouble to compute and output one of the
possible maximum nestings, which is output on the line
just before the maximum nesting length.


File:	   crates.txt
Author:	   Shai Simonson <shai@stonehill.edu>
	   with minor revisions by
           Bob Walton <walton@seas.harvard.edu>
Date:	   Sat Oct  5 06:10:25 EDT 2013

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: 2013/10/05 12:05:21 $
    $RCSfile: crates.txt,v $
    $Revision: 1.3 $