You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 32.0 MB

# Problem
Please note the non-standard memory limit.

There are $$$n$$$ problems numbered with integers from $$$1$$$ to $$$n$$$. $$$i$$$-th problem has the complexity $$$c_i = 2^i$$$, tag $$$tag_i$$$ and score $$$s_i$$$.

After solving the problem $$$i$$$ it's allowed to solve problem $$$j$$$ if and only if $$$\text{IQ} < |c_i - c_j|$$$ and $$$tag_i \neq tag_j$$$. After solving it your $$$\text{IQ}$$$ changes and becomes $$$\text{IQ} = |c_i - c_j|$$$ and you gain $$$|s_i - s_j|$$$ points.

Any problem can be the first. You can solve problems in any order and as many times as you want.

Initially your $$$\text{IQ} = 0$$$. Find the maximum number of points that can be earned.

## Input Format
The first line contains a single integer $$$t$$$ $$$(1 \le t \le 100)$$$  — the number of test cases.

The first line of each test case contains an integer $$$n$$$ $$$(1 \le n \le 5000)$$$  — the number of problems.

The second line of each test case contains $$$n$$$ integers $$$tag_1, tag_2, \ldots, tag_n$$$ $$$(1 \le tag_i \le n)$$$  — tags of the problems.

The third line of each test case contains $$$n$$$ integers $$$s_1, s_2, \ldots, s_n$$$ $$$(1 \le s_i \le 10^9)$$$  — scores of the problems.

It's guaranteed that sum of $$$n$$$ over all test cases does not exceed $$$5000$$$.

## Output Format
For each test case print a single integer  — the maximum number of points that can be earned.

## Examples
```input
5
4
1 2 3 4
5 10 15 20
4
1 2 1 2
5 10 15 20
4
2 2 4 1
2 8 19 1
2
1 1
6 9
1
1
666
```
```output
35
30
42
0
0
```

## Note
In the first test case optimal sequence of solving problems is as follows:

1. $$$1 \rightarrow 2$$$, after that total score is $$$5$$$ and $$$\text{IQ} = 2$$$
2. $$$2 \rightarrow 3$$$, after that total score is $$$10$$$ and $$$\text{IQ} = 4$$$
3. $$$3 \rightarrow 1$$$, after that total score is $$$20$$$ and $$$\text{IQ} = 6$$$
4. $$$1 \rightarrow 4$$$, after that total score is $$$35$$$ and $$$\text{IQ} = 14$$$

In the second test case optimal sequence of solving problems is as follows:

1. $$$1 \rightarrow 2$$$, after that total score is $$$5$$$ and $$$\text{IQ} = 2$$$
2. $$$2 \rightarrow 3$$$, after that total score is $$$10$$$ and $$$\text{IQ} = 4$$$
3. $$$3 \rightarrow 4$$$, after that total score is $$$15$$$ and $$$\text{IQ} = 8$$$
4. $$$4 \rightarrow 1$$$, after that total score is $$$35$$$ and $$$\text{IQ} = 14$$$

In the third test case optimal sequence of solving problems is as follows:

1. $$$1 \rightarrow 3$$$, after that total score is $$$17$$$ and $$$\text{IQ} = 6$$$
2. $$$3 \rightarrow 4$$$, after that total score is $$$35$$$ and $$$\text{IQ} = 8$$$
3. $$$4 \rightarrow 2$$$, after that total score is $$$42$$$ and $$$\text{IQ} = 12$$$

Now solve the problem and return the code.