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: 512.0 MB

# Problem
The hero is addicted to glory, and is fighting against a monster.

The hero has $$$n$$$ skills. The $$$i$$$-th skill is of type $$$a_i$$$ (either fire or frost) and has initial damage $$$b_i$$$.

The hero can perform all of the $$$n$$$ skills in any order (with each skill performed exactly once). When performing each skill, the hero can play a magic as follows:

- If the current skill immediately follows another skill of a different type, then its damage is doubled.

1. If a skill of type fire and with initial damage $$$c$$$ is performed immediately after a skill of type fire, then it will deal $$$c$$$ damage;
2. If a skill of type fire and with initial damage $$$c$$$ is performed immediately after a skill of type frost, then it will deal $$$2c$$$ damage;
3. If a skill of type frost and with initial damage $$$c$$$ is performed immediately after a skill of type fire, then it will deal $$$2c$$$ damage;
4. If a skill of type frost and with initial damage $$$c$$$ is performed immediately after a skill of type frost , then it will deal $$$c$$$ damage.

Your task is to find the maximum damage the hero can deal.

## Input Format
Each test contains multiple test cases. The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 10^5$$$) — the number of test cases. The following lines contain the description of each test case.

The first line of each test case contains an integer $$$n$$$ ($$$1 \leq n \leq 10^5$$$), indicating the number of skills.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \leq a_i \leq 1$$$), where $$$a_i$$$ indicates the type of the $$$i$$$-th skill. Specifically, the $$$i$$$-th skill is of type fire if $$$a_i = 0$$$, and of type frost if $$$a_i = 1$$$.

The third line of each test case contains $$$n$$$ integers $$$b_1, b_2, \dots, b_n$$$ ($$$1 \leq b_i \leq 10^9$$$), where $$$b_i$$$ indicates the initial damage of the $$$i$$$-th skill.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

## Output Format
For each test case, output the maximum damage the hero can deal.

## Examples
```input
4
4
0 1 1 1
1 10 100 1000
6
0 0 0 1 1 1
3 4 5 6 7 8
3
1 1 1
1000000000 1000000000 1000000000
1
1
1
```
```output
2112
63
3000000000
1
```

## Note
In the first test case, we can order the skills by $$$[3, 1, 4, 2]$$$, and the total damage is $$$100 + 2 \times 1 + 2 \times 1000 + 10 = 2112$$$.

In the second test case, we can order the skills by $$$[1, 4, 2, 5, 3, 6]$$$, and the total damage is $$$3 + 2 \times 6 + 2 \times 4 + 2 \times 7 + 2 \times 5 + 2 \times 8 = 63$$$.

In the third test case, we can order the skills by $$$[1, 2, 3]$$$, and the total damage is $$$1000000000 + 1000000000 + 1000000000 = 3000000000$$$.

In the fourth test case, there is only one skill with initial damage $$$1$$$, so the total damage is $$$1$$$.

Now solve the problem and return the code.