A. Array Balancingtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given two arrays of length n: a_1, a_2, \dots, a_n and b_1, b_2, \dots, b_n.You can perform the following operation any number of times:   Choose integer index i (1 \le i \le n);  Swap a_i and b_i. What is the minimum possible sum |a_1 - a_2| + |a_2 - a_3| + \dots + |a_{n-1} - a_n| + |b_1 - b_2| + |b_2 - b_3| + \dots + |b_{n-1} - b_n| (in other words, \sum\limits_{i=1}^{n - 1}{\left(|a_i - a_{i+1}| + |b_i - b_{i+1}|\right)}) you can achieve after performing several (possibly, zero) operations?InputThe 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.OutputFor 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)}.ExampleInput
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
Output
0
8
218
NoteIn 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.
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

0 8 218 
['greedy', 'math', '*800']