D. Absolute Beautytime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputKirill has two integer arrays a_1,a_2,\ldots,a_n and b_1,b_2,\ldots,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 \leq i < j \leq n) and swap the values of b_i and b_j. Help him find the maximum possible absolute beauty of the array b after performing at most one swap.InputEach 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.OutputFor each test case, output one integer — the maximum possible absolute beauty of the array b after no more than one swap.ExampleInput
631 3 53 3 321 21 221 22 141 2 3 45 6 7 8101 8 2 5 3 5 3 1 1 32 9 2 4 8 2 3 5 3 1347326 6958 3586533587 35863 59474Output
4
2
2
16
31
419045
NoteIn 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.
631 3 53 3 321 21 221 22 141 2 3 45 6 7 8101 8 2 5 3 5 3 1 1 32 9 2 4 8 2 3 5 3 1347326 6958 3586533587 35863 59474
4 2 2 16 31 419045 
['greedy', 'math', '*1900']