CF1898D Absolute Beauty

Kirill has two integer arrays $a_1,a_2,…,a_n$ and $b_1,b_2,…,b_n$ of length $n$. He defines the _absolute beauty_ of the array $b$ as $$ \sum_{i=1}^n|a_i-b_i| $$ Here, $|x|$ denotes the absolute value of $x$. Kirill can perform the following operation **at most once**: - select two indices $i$ and $j$ ($1≤i

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \leq t \leq 10\,000 $ ). The description of test cases follows. The first line of each test case contains a single integer $ n $ ( $ 2\leq n\leq 2\cdot 10^5 $ ) — the length of the arrays $ a $ and $ b $ . The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1\leq a_i\leq 10^9 $ ) — the array $ a $ . The third line of each test case contains $ n $ integers $ b_1, b_2, \ldots, b_n $ ( $ 1\leq b_i\leq 10^9 $ ) — the array $ b $ . It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2\cdot 10^5 $ .

For each test case, output one integer — the maximum possible absolute beauty of the array $ b $ after no more than one swap.

In the first test case, each of the possible swaps does not change the array $ b $ . In the second test case, the absolute beauty of the array $ b $ without performing the swap is $ |1-1| + |2-2| = 0 $ . After swapping the first and the second element in the array $ b $ , the absolute beauty becomes $ |1-2| + |2-1| = 2 $ . These are all the possible outcomes, hence the answer is $ 2 $ . In the third test case, it is optimal for Kirill to not perform the swap. Similarly to the previous test case, the answer is $ 2 $ . In the fourth test case, no matter what Kirill does, the absolute beauty of $ b $ remains equal to $ 16 $ .