题面翻译

两个长度均为 $n$ 的数组 $a,b$。一次操作可以选择两个下标 $i,j$，交换 $b_i,b_j$。你需要进行最多一次操作，最大化 $\sum \limits_{i=1}^n |a_i-b_i|$。

题目描述

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

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.

输入格式

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 $2\cdot 10^5$ .

输出格式

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

样例 #1

样例输入 #1

6
3
1 3 5
3 3 3
2
1 2
1 2
2
1 2
2 1
4
1 2 3 4
5 6 7 8
10
1 8 2 5 3 5 3 1 1 3
2 9 2 4 8 2 3 5 3 1
3
47326 6958 358653
3587 35863 59474

样例输出 #1

4
2
2
16
31
419045

提示

In the first test case, each of the possible swaps does not change the array $b$ .

In the second test case, the absolute beauty of the array $b$ without performing the swap is $|1-1| + |2-2| = 0$ . After swapping the first and the second element in the array $b$ , the absolute beauty becomes $|1-2| + |2-1| = 2$ . These are all the possible outcomes, hence the answer is $2$ .

In the third test case, it is optimal for Kirill to not perform the swap. Similarly to the previous test case, the answer is $2$ .

In the fourth test case, no matter what Kirill does, the absolute beauty of $b$ remains equal to $16$ .