Tokitsukaze and Two Colorful Tapes

题意翻译

有两个颜色排列$a$和$b$，两个排列中相同颜色的位置可以填充$1$~$n$中的同一个数字且不可重复 如果使得最后数字序列为：$numa_{i},numb_{i}$，要求最大化$\sum_{i-1}^{n}{|numa_{i}-numb_{i}|}$

题目描述

Tokitsukaze has two colorful tapes. There are $ n $ distinct colors, numbered $ 1 $ through $ n $ , and each color appears exactly once on each of the two tapes. Denote the color of the $ i $ -th position of the first tape as $ ca_i $ , and the color of the $ i $ -th position of the second tape as $ cb_i $ . Now Tokitsukaze wants to select each color an integer value from $ 1 $ to $ n $ , distinct for all the colors. After that she will put down the color values in each colored position on the tapes. Denote the number of the $ i $ -th position of the first tape as $ numa_i $ , and the number of the $ i $ -th position of the second tape as $ numb_i $ . For example, for the above picture, assuming that the color red has value $ x $ ( $ 1 \leq x \leq n $ ), it appears at the $ 1 $ -st position of the first tape and the $ 3 $ -rd position of the second tape, so $ numa_1=numb_3=x $ . Note that each color $ i $ from $ 1 $ to $ n $ should have a distinct value, and the same color which appears in both tapes has the same value. After labeling each color, the beauty of the two tapes is calculated as $ $\sum_{i=1}^{n}|numa_i-numb_i|. $ $ Please help Tokitsukaze to find the highest possible beauty.

输入输出格式

输入格式

The first contains a single positive integer $ t $ ( $ 1 \leq t \leq 10^4 $ ) — the number of test cases. For each test case, the first line contains a single integer $ n $ ( $ 1\leq n \leq 10^5 $ ) — the number of colors. The second line contains $ n $ integers $ ca_1, ca_2, \ldots, ca_n $ ( $ 1 \leq ca_i \leq n $ ) — the color of each position of the first tape. It is guaranteed that $ ca $ is a permutation. The third line contains $ n $ integers $ cb_1, cb_2, \ldots, cb_n $ ( $ 1 \leq cb_i \leq n $ ) — the color of each position of the second tape. It is guaranteed that $ cb $ is a permutation. 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, print a single integer — the highest possible beauty.

输入输出样例

输入样例 #1

3
6
1 5 4 3 2 6
5 3 1 4 6 2
6
3 5 4 6 2 1
3 6 4 5 2 1
1
1
1

输出样例 #1

18
10
0

说明

An optimal solution for the first test case is shown in the following figure: The beauty is $ \left|4-3 \right|+\left|3-5 \right|+\left|2-4 \right|+\left|5-2 \right|+\left|1-6 \right|+\left|6-1 \right|=18 $ . An optimal solution for the second test case is shown in the following figure: The beauty is $ \left|2-2 \right|+\left|1-6 \right|+\left|3-3 \right|+\left|6-1 \right|+\left|4-4 \right|+\left|5-5 \right|=10 $ .