A15161 | 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.

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 $2 \cdot 10^{5}$ .

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