BABTWR  Tower of Babylon
Apart from the Hanging Gardens the Babylonians (around 3000539 b.c.) built the Tower of Babylon as well. The tower was meant to reach the sky, but the project failed because of a confusion of language imposed from much higher above.
For the 2638th anniversary a model of the tower will be rebuilt. n different types of blocks are available. Each one of them may be duplicated as many times as you like. Each type has a height y, a width x and a depth z. The blocks are to be stacked one upon eachother so that the resulting tower is as high as possible. Of course the blocks can be rotated as desired before stacking. However for reasons of stability a block can only be stacked upon another if both of its baselines are shorter.
Input
The number of types of blocks n is located in the first line of each test case. On the subsequent n lines the height y_{i}, the width x_{i} and the depth z_{i} of each type of blocks are given. There are never more than 30 different types available.
There are many test cases, which come one by one. Input terminates with n = 0.
Edited: You can assume that max(x_{i}, y_{i}, z_{i}) <= 2500.
Output
For each test case your program should output one line with the height of the highest possible tower.
Example
Sample input: 5 31 41 59 26 53 58 97 93 23 84 62 64 33 83 27 1 1 1 1 0 Sample output: 342 1
hide comments
ashish22_dwd:
20161007 15:26:38
My 50th with this nice problem :) 

hamjosh1:
20160925 09:26:55
easy :'D


praval_singhal:
20160630 13:24:20
AC in one go. TopDown is great. 

Mohit Rathore:
20150829 10:00:17
This problem is just awesome! 

agaurav77:
20141231 15:49:11
This one is a nice DP question. Those who are confused about rotations, here's a hint : the number of rotations possible depend on the dimensions. For example, <1,1,1> has 1 rotation, whereas <1,2,3> has 6 rotations. 

Rajat (1307086):
20141229 05:04:23
Nelson number shows up with this DP. Do not cross check case 1. It is correct. use it to check your solution. 

Archit Jain:
20141224 20:21:04
nice dp 

DEEPAK KUMAR SINGH:
20141218 16:55:57
1st century for me on SPOJ....Completed 100 with a dp... Last edit: 20141218 16:56:35 

mayank:
20141215 10:04:58
DP! nice! 

robert:
20130423 03:08:59
Note: "a block can only be stacked upon another if both of its baselines are shorter"

Added by:  MichaĆ Czuczman 
Date:  20040706 
Time limit:  3s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  Swiss Olympiad in Informatics 2004 