FASHION  Fashion Shows
A fashion show rates participants according to their level of hotness. Two different fashion shows were organized, one for men and the other for women. A date for the third is yet to be decided ;) .
Now the results of both fashion shows are out. The participants of both the fashion shows have decided to date each other, but as usual they have difficuly in choosing their partners. The Maximum Match dating serive (MMDS) comes to their rescue and matches them in such a way that that maximizes the hotness bonds for all couples.
If a man has been rated at hotness level x and a women at hotness level y, the value of their hotness bond is x*y.
Both fashion shows contain N participants each. MMDS has done its job and your job is to find the sum of hotness bonds for all the couples that MMDS has proposed.
Input
The first line of the input contains an integer t, the number of test cases. t test cases follow.
Each test case consists of 3 lines:
 The first line contains a single integer N (1 <= N <= 1000).
 The second line contains N integers separated by single spaces denoting the hotness levels of the men.
 The third line contains N integers separated by single spaces denoting the hotness levels of the women.
All hotness ratings are on a scale of 0 to 10.
Output
For each test case output a single line containing a single integer denoting the sum of the hotness bonds for all pairs that MMDS has proposed.
Example
Input: 2 2 1 1 3 2 3 2 3 2 1 3 2 Output: 5 15
hide comments
Aradhya:
20120407 09:19:13
:O what the f.. by bubble sort it gotAC.. and by my heap sort it gives wrong answer 

HÃ©lder Moreira:
20120208 23:22:08
http://ideone.com/fncSk


Ajay Gupta:
20120204 20:55:50
can i have some more test cases pls...i'm getting it correct on my machine but shows


Baskara Nur Patria:
20111206 10:00:18
please give me some test case, runs well on my computer, but still getting WA 

Mark Fulbright:
20110404 04:50:52
Yes, you must maximize the sum of the hotness bonds for the couples by changing the pairs if necessary. 

adri ramadhan:
20110327 04:09:13
i don't get the output, anybody care to explain? 

Alexander:
20101020 15:46:08
On an interesting side note: the maximising principle underlying this problem generalises to almosteverywhere finite functions on sigmafinite measure spaces by a theorem of Hardy and Littlewood, see Theorem II.2.2 in C. Bennett, R. Sharpley, "Interpolation of Operators" Last edit: 20101020 15:46:41 

Bill Black:
20090706 05:24:03
Although MMDS proposes couples, it in no way ensures that the couples match up to produce a maximum hotness. Nay, such work is left up to the programmer in a typical "oh, I thought I mentioned that to you yesterday" style. :P 

~!(*(@*!@^&:
20090416 15:20:09
More clarification : a[i] may not match with b[i]. 
Added by:  Matthew Reeder 
Date:  20061029 
Time limit:  0.970s 
Source limit:  30000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  AlKhawarizm 2006 