MAIN112 - Re-Arrange II

For a sequence of N integers, A1, A2, ... AN

We can calculate the stability factor P, as

P = sum of all (abs(Ai-Ai-1)*C[i]) where 2 <= i <= N

C[i] is the cost of putting a number at position i

Your task is find the minimum P for the given N numbers considering all the different permutations of them.

Input

First line contains an integer T (1<=T<=10) which denotes the total number of test cases. Each test case consists of three lines.

The first line contains the integer N (1<=N<=15). The second line contains a space separated list of N integers (<150) which denote the given set of numbers.

The third line contains a space separated list of N integers. The ith integer on this line denotes the value for C[i] (1 <= C[i] < 150)

Output

For each test case, print the minimum possible value of P considering all permutations of the given numbers.

Example

Input:
1
5
1 8 3 6 5
1 2 3 4 5

Output
24

One of the possible permutation of given numbers which has p = 24 is 1, 3, 5, 6, 8


Added by:amit karmakar
Date:2011-08-15
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:own problem used in - http://www.spoj.pl/MAIN11/

hide comments
2023-05-11 04:56:26
Do not permutate the cost array, otherwise you will get 21 instead of 24 in the given test case.
2019-11-21 19:53:21
AC in my first attempt !
nice bitmask dp ...
good one for beginner
2019-06-15 15:16:21
AC in 2nd attempt :D
2017-07-31 16:31:19
@Divyank no, there is no use for cost[0]
2015-07-07 15:53:30 ankit kumar
@bitwise ans in your case should be abs(6-5)*2+abs(8-6)*3+abs(1-8)*4+abs(3-1)*5>21&&24.
2015-07-02 12:13:34 bitwise
why can't the minimum possible value be 21 ??????
for :
5 6 8 1 3
8 6 5 3 1
2014-12-23 13:31:52 Divyank Duvedi
Is there any use of cost[0]?
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