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: 256.0 MB

# Problem
You are given a permutation $$$p$$$ of length $$$n$$$, an array of $$$m$$$ distinct integers $$$a_1, a_2, \ldots, a_m$$$ ($$$1 \le a_i \le n$$$), and an integer $$$d$$$.

Let $$$\mathrm{pos}(x)$$$ be the index of $$$x$$$ in the permutation $$$p$$$. The array $$$a$$$ is not good if

- $$$\mathrm{pos}(a_{i}) < \mathrm{pos}(a_{i + 1}) \le \mathrm{pos}(a_{i}) + d$$$ for all $$$1 \le i < m$$$.

For example, with the permutation $$$p = [4, 2, 1, 3, 6, 5]$$$ and $$$d = 2$$$:

- $$$a = [2, 3, 6]$$$ is a not good array.
- $$$a = [2, 6, 5]$$$ is good because $$$\mathrm{pos}(a_1) = 2$$$, $$$\mathrm{pos}(a_2) = 5$$$, so the condition $$$\mathrm{pos}(a_2) \le \mathrm{pos}(a_1) + d$$$ is not satisfied.
- $$$a = [1, 6, 3]$$$ is good because $$$\mathrm{pos}(a_2) = 5$$$, $$$\mathrm{pos}(a_3) = 4$$$, so the condition $$$\mathrm{pos}(a_2) < \mathrm{pos}(a_3)$$$ is not satisfied.

In one move, you can swap two adjacent elements of the permutation $$$p$$$. What is the minimum number of moves needed such that the array $$$a$$$ becomes good? It can be shown that there always exists a sequence of moves so that the array $$$a$$$ becomes good.

A permutation is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array) and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$, but there is $$$4$$$ in the array).

## Input Format
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains three integers $$$n$$$, $$$m$$$ and $$$d$$$ ($$$2\leq n \leq 10^5$$$, $$$2\leq m\leq n$$$, $$$1 \le d \le n$$$), the length of the permutation $$$p$$$, the length of the array $$$a$$$ and the value of $$$d$$$.

The second line contains $$$n$$$ integers $$$p_1, p_2, \ldots, p_n$$$ ($$$1\leq p_i \leq n$$$, $$$p_i \ne p_j$$$ for $$$i \ne j$$$).

The third line contains $$$m$$$ distinct integers $$$a_1, a_2, \ldots, a_m$$$ ($$$1\leq a_i \leq n$$$, $$$a_i \ne a_j$$$ for $$$i \ne j$$$).

The sum of $$$n$$$ over all test cases doesn't exceed $$$5 \cdot 10^5$$$.

## Output Format
For each test case, print the minimum number of moves needed such that the array $$$a$$$ becomes good.

## Examples
```input
5
4 2 2
1 2 3 4
1 3
5 2 4
5 4 3 2 1
5 2
5 3 3
3 4 1 5 2
3 1 2
2 2 1
1 2
2 1
6 2 4
1 2 3 4 5 6
2 5
```
```output
1
3
2
0
2
```

## Note
In the first case, $$$pos(a_1)=1$$$, $$$pos(a_2)=3$$$. To make the array good, one way is to swap $$$p_3$$$ and $$$p_4$$$. After that, the array $$$a$$$ will be good because the condition $$$\mathrm{pos}(a_2) \le \mathrm{pos}(a_1) + d$$$ won't be satisfied.

In the second case, $$$pos(a_1)=1$$$, $$$pos(a_2)=4$$$. The $$$3$$$ moves could be:

1. Swap $$$p_3$$$ and $$$p_4$$$.
2. Swap $$$p_2$$$ and $$$p_3$$$.
3. Swap $$$p_1$$$ and $$$p_2$$$.

In the third case, $$$pos(a_1)=1$$$, $$$pos(a_2)=3$$$, $$$pos(a_3)=5$$$. The $$$2$$$ moves can be:

1. Swap $$$p_4$$$ and $$$p_5$$$.
2. Swap $$$p_3$$$ and $$$p_4$$$.

In the fourth case, $$$pos(a_1)=2$$$, $$$pos(a_2)=1$$$. The array $$$a$$$ is already good.

In the fifth case, $$$pos(a_1)=2$$$, $$$pos(a_2)=5$$$. The $$$2$$$ moves are:

1. Swap $$$p_1$$$ and $$$p_2$$$.
2. Swap $$$p_5$$$ and $$$p_6$$$.

Now solve the problem and return the code.