CF1677C.Tokitsukaze and Two Colorful Tapes

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.

Tokitsukaze 有两条彩色胶带。共有 $n$ 种互不相同的颜色，编号为 $1$ 到 $n$，且每种颜色在每条胶带上恰好出现一次。记第一条胶带上第 $i$ 个位置的颜色为 $ca_i$，第二条胶带上第 $i$ 个位置的颜色为 $cb_i$。

现在，Tokitsukaze 想要为每种颜色分配一个 $1$ 到 $n$ 之间的整数值，且所有颜色的值互不相同。随后，她将把这些数值填入胶带上对应颜色的位置中。记第一条胶带上第 $i$ 个位置的数值为 $numa_i$，第二条胶带上第 $i$ 个位置的数值为 $numb_i$。

例如，在上图中，假设红色对应值 $x$（其中 $1 \leq x \leq n$），而红色出现在第一条胶带的第 $1$ 个位置和第二条胶带的第 $3$ 个位置，则有 $numa_1 = numb_3 = x$。

注意：颜色 $1$ 至 $n$ 的取值必须互不相同，且同一种颜色（在两条胶带上均出现）必须赋予相同的数值。

完成颜色赋值后，两条胶带的“美观度”定义为

$$\sum_{i=1}^{n}|numa_i - numb_i|。$$

请帮助 Tokitsukaze 求出可能达到的最大美观度。

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 $2 \cdot 10^{5}$.

第一行包含一个正整数 $t$（$1 \leq t \leq 10^4$）——测试用例的数量。

对于每个测试用例，第一行包含一个整数 $n$（$1\leq n \leq 10^5$）——颜色的种类数。

第二行包含 $n$ 个整数 $ca_1, ca_2, \ldots, ca_n$（$1 \leq ca_i \leq n$）——第一条胶带每个位置的颜色。保证 $ca$ 是一个排列。

第三行包含 $n$ 个整数 $cb_1, cb_2, \ldots, cb_n$（$1 \leq cb_i \leq n$）——第二条胶带每个位置的颜色。保证 $cb$ 是一个排列。

保证所有测试用例的 $n$ 之和不超过 $2 \cdot 10^{5}$。

For each test case, print a single integer — the highest possible beauty.

对于每个测试用例，输出一个整数——可能达到的最高美丽值。

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 $\left|2-2 \right|+\left|1-6 \right|+\left|3-3 \right|+\left|6-1 \right|+\left|4-4 \right|+\left|5-5 \right|=10$.

第一个测试用例的最优解如下图所示：

其美观度为 $\left|4-3 \right|+\left|3-5 \right|+\left|2-4 \right|+\left|5-2 \right|+\left|1-6 \right|+\left|6-1 \right|=18$。

第二个测试用例的最优解如下图所示：

其美观度为 $\left|2-2 \right|+\left|1-6 \right|+\left|3-3 \right|+\left|6-1 \right|+\left|4-4 \right|+\left|5-5 \right|=10$。