## 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 scolar_fuad: 2019-11-21 19:53:21 AC in my first attempt ! nice bitmask dp ... good one for beginner walter_whitee: 2019-06-15 15:16:21 AC in 2nd attempt :D hodobox: 2017-07-31 16:31:19 @Divyank no, there is no use for cost ankit kumar: 2015-07-07 15:53:30 @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. bitwise: 2015-07-02 12:13:34 why can't the minimum possible value be 21 ?????? for : 5 6 8 1 3 8 6 5 3 1 Divyank Duvedi: 2014-12-23 13:31:52 Is there any use of cost?