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
bikram6928:
20170125 09:43:21
It seems that the MMDS doesn't work. It only returns the entries


Varun Goyal:
20170122 17:50:51
Greedy proof by Rearrangement Inequality 

scorpion_ajay:
20161217 10:39:44
do read the statement carefully, sorting costed me 1 WA _ 

abhi_upadhyay:
20161207 18:56:35
what's the reason for sorting?


the_phoenixx:
20161030 11:12:27
AC in 1st go 

arpitscoding:
20160826 19:34:08
SORRRTTTTT!!! Then multiply. 

Sarvajeet Suman:
20160731 15:09:59
Rearrangement_inequality, That's all you need. 

hassanarif63:
20160610 06:52:00
AC_in _1_go 

get_right_jr:
20160607 14:41:21
the EASIEST problem I've ever solved!!! 

code0monkey1:
20160606 23:52:15
Apparently the Maximum Match dating serive (MMDS) has not done it's job properly , so you need to sort them according to hotness yourself 
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 