C. Tokitsukaze and Two Colorful Tapestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputTokitsukaze 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. InputThe 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}.OutputFor each test case, print a single integer — the highest possible beauty.ExampleInput
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
Output
18
10
0
NoteAn 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.
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

18 10 0 
['constructive algorithms', 'dfs and similar', 'graphs', 'greedy', '*1900']