Increase/Decrease/Copy
Description
You are given two integer arrays: array $a$ of length $n$ and array $b$ of length $n+1$.
You can perform the following operations any number of times in any order:
- choose any element of the array $a$ and increase it by $1$;
- choose any element of the array $a$ and decrease it by $1$;
- choose any element of the array $a$, copy it and append the copy to the end of the array $a$.
Your task is to calculate the minimum number of aforementioned operations (possibly zero) required to transform the array $a$ into the array $b$. It can be shown that under the constraints of the problem, it is always possible.
The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.
Each test case consists of three lines:
- the first line contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$);
- the second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$);
- the third line contains $n + 1$ integers $b_1, b_2, \dots, b_{n + 1}$ ($1 \le b_i \le 10^9$).
Additional constraint on the input: the sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$.
For each test case, print a single integer — the minimum number of operations (possibly zero) required to transform the array $a$ into the array $b$.
Input
The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.
Each test case consists of three lines:
- the first line contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$);
- the second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$);
- the third line contains $n + 1$ integers $b_1, b_2, \dots, b_{n + 1}$ ($1 \le b_i \le 10^9$).
Additional constraint on the input: the sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$.
Output
For each test case, print a single integer — the minimum number of operations (possibly zero) required to transform the array $a$ into the array $b$.
3
1
2
1 3
2
3 3
3 3 3
4
4 2 1 2
2 1 5 2 3
3
1
8
Note
In the first example, you can transform $a$ into $b$ as follows: $[2] \rightarrow [2, 2] \rightarrow [1, 2] \rightarrow [1, 3]$.