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 python3.

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:
```python
<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.