BACKPACK  Dab of Backpack
One day Blue Mary goes to a nearby supermarket to buy some goods. She has a backpack, whose capacity is VMax. She finds that there are many goods in the market, each has a volume V_{i}(it will always be a multiple of 10 and less than 10000) and an importance C_{i}(1<= C_{i} <=5). Since she has almost unlimited money, the only problem she is to solve is how to choose goods such that the total volume won't exceed the capacity of the backpack and the sum of the product of the volume and the importance of each good is maximum. To be an excellent mathematician, she comes up with the answer quickly, and now she wants you to do a harder task. There are two kinds of goods: main goods and attachments. If you want to buy an attachment you must buy its main good before.
Input
Multiple test cases, the number of them is given in the very first line.
For each test case:
The first line contains two spaceseparated integers VMax (1<=VMax<=32000) and the number of the goods N (1<=N<=60). N lines follow, each contains three spaceseparated integers V_{i}, C_{i} and a integer u. If u is not 0, this good is an attachment of good u(as the order in the input file).
To make the problem not too difficult, Blue Mary tells you that:
(A) An attachment won't have any attachments which belong to it.
(B) A main good will always have less than 3 attachments.
Output
For each test case:
The first and the only line contains a single integer denoted the answer.
Example
Input: 1 1000 5 800 2 0 400 5 1 300 5 1 400 3 0 500 2 0 Output: 2200
hide comments
natsu:
20130531 14:14:38
Finally got AC, very good problem thanks to the problemsetter


DivineAtheist:
20130108 22:59:45
finally got AC.....after trying too hard...nice problem...:) 

Mukesh Yadav:
20121207 21:30:00
@ankit You can buy as many attachments as you want, even no one , but satisfying the condition that you have bought their main good ! 

Romal Thoppilan:
20121013 12:46:43
Are the goods unbounded or single(limited) , pls mention it


sriankit:
20120725 06:02:39
can i buy a particular attachment and the main good..???


manushree:
20111006 23:29:50
Plz explain the questn properly! Are repetitions allowed? 

Nagy Mohamed:
20100713 15:50:45
@cenation : no 

nishaanth:
20100525 09:11:56
if we take a main good are we forced to take its attachments also?? 

Lewin Gan:
20100407 02:21:59
very nice problem 
Added by:  Fudan University Problem Setters 
Date:  20071103 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: C99 ERL JSRHINO 
Resource:  Based on a Problem from Chinese National Olympiad in Informatics in Province 2006 