CF1661A Array Balancing

You 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: 1. Choose integer index $ i $ ( $ 1 \le i \le n $ ); 2. 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?

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 $ .

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)} $ .

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 $ .