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
rituraj: 2014-08-07 19:16:12

got green in 2nd submission wasnt mentioned that sum has to be maximised credit :comments.

ravi: 2014-08-06 20:31:01

AC in 2nd go...

mohsin mohammad: 2014-08-03 19:19:01

hmmmm AC in first go.Good problem of hashing.

Madhur Bhargava: 2014-07-28 11:22:00

AC in 2nd go. We need to understand the maximize clause. Thanks to VARUN KUMARE for test cases.

Siddhant Somani: 2014-07-16 17:41:08

Got AC in second attempt because I had ignored the "maximise" clause !
Question should have been clear.

heena rana: 2014-07-04 20:42:20

cakewalk AC in one go... :D :D

Mitch Schwartz: 2014-07-02 17:05:14

@Kumar Shubham: SPOJ allows you to read the compilation error.

Kumar Shubham: 2014-07-02 16:26:09

My code shows compilation error here, it is running quite smoothly when compiled in my own machine with gnu-gcc compiler, though. Please help.

Verma Rahul Omprakash: 2014-06-12 19:43:03

Who so ever has framed the question should clarify that the sum has to be maximized....

Krish: 2014-05-20 11:54:17

Provide TestCase please


Added by:Matthew Reeder
Date:2006-10-29
Time limit:0.970s
Source limit:30000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:Al-Khawarizm 2006