Array Balancing

Description:

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 4000$$$) — the number of test cases. Then, $$$t$$$ test cases follow.

The first line of each test case contains the single integer $$$n$$$ ($$$2 \le n \le 25$$$) — the length of arrays $$$a$$$ and $$$b$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the array $$$a$$$.

The third line of each test case contains $$$n$$$ integers $$$b_1, b_2, \dots, b_n$$$ ($$$1 \le b_i \le 10^9$$$) — the array $$$b$$$.

Output:

For each test case, print one integer — the minimum possible sum $$$\sum\limits_{i=1}^{n-1}{\left(|a_i - a_{i+1}| + |b_i - b_{i+1}|\right)}$$$.

Sample Input:

3
4
3 3 10 10
10 10 3 3
5
1 2 3 4 5
6 7 8 9 10
6
72 101 108 108 111 44
10 87 111 114 108 100

Sample Output:

0
8
218

Note:

In the first test case, we can, for example, swap $$$a_3$$$ with $$$b_3$$$ and $$$a_4$$$ with $$$b_4$$$. We'll get arrays $$$a = [3, 3, 3, 3]$$$ and $$$b = [10, 10, 10, 10]$$$ with sum $$$3 \cdot |3 - 3| + 3 \cdot |10 - 10| = 0$$$.

In the second test case, arrays already have minimum sum (described above) equal to $$$|1 - 2| + \dots + |4 - 5| + |6 - 7| + \dots + |9 - 10|$$$ $$$= 4 + 4 = 8$$$.

In the third test case, we can, for example, swap $$$a_5$$$ and $$$b_5$$$.