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
Alien: 2013-06-08 03:13:31

EASY1 , but question does not clarify the sorting ...for maximizing the sum

aar: 2013-06-07 19:38:21

MMDS has not done its job..

Erti-Chris Eelmaa: 2013-05-27 19:25:19

Very easy. Took me 3-4 minutes.

Filipe Bittencourt [UNIFEI]: 2013-04-17 04:17:42

MMDS hasn't done it's job!
Unfortunately got my first WA because of this wrong information!
Easily solved.

Sivaraman Nagarajan: 2013-02-23 16:51:45

Move it to tutorial

Mahavir Chopra: 2013-01-04 15:34:17

upload is not wrking

Hasil Sharma: 2013-01-03 04:24:03

Python nails this question !!! but seriously question is under specified !!! MMDS hasn't done it's job :P

VARUN KUMARE: 2013-01-01 11:56:41

hey guys! also try it...
I/P:
2
3
2 5 4
6 9 1
4
7 8 9 4
1 2 4 3
O/P:
71
78

Haijun Deng: 2012-12-11 07:18:23

More test cases needed

Gandaro: 2012-09-08 10:29:43

“MMDS has done its job and your job is to find the sum of hotness bonds for all the couples that MMDS has proposed.”

“Yes, you must maximize the sum of the hotness bonds for the couples by changing the pairs if necessary.”

This is contradictory!


Added by:Matthew Reeder
Date:2006-10-29
Time limit:1s
Source limit:30000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:Al-Khawarizm 2006