A16316 | Absolute Beauty

Kirill has two integer arrays $a_1,a_2,…,a_n$ and $b_1,b_2,…,b_n$ of length $n$. He defines the _absolute beauty_ of the array $b$ as
$$ \sum_{i=1}^n|a_i-b_i| $$
Here, $|x|$ denotes the absolute value of $x$.

Kirill can perform the following operation **at most once**:

- select two indices $i$ and $j$ ($1≤i<j≤n$) and swap the values of $b_i$ and $b_j$.

Help him find the maximum possible absolute beauty of the array $b$ after performing **at most one** swap.

Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \leq t \leq 10\,000$ ). The description of test cases follows.

The first line of each test case contains a single integer $n$ ( $2\leq n\leq 2\cdot 10^5$ ) — the length of the arrays $a$ and $b$ .

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1\leq a_i\leq 10^9$ ) — the array $a$ .

The third line of each test case contains $n$ integers $b_1, b_2, \ldots, b_n$ ( $1\leq b_i\leq 10^9$ ) — the array $b$ .

It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot 10^5$ .

For each test case, output one integer — the maximum possible absolute beauty of the array $b$ after no more than one swap.