B. Interesting Sumtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an array a that contains n integers. You can choose any proper subsegment a_l, a_{l + 1}, \ldots, a_r of this array, meaning you can choose any two integers 1 \le l \le r \le n, where r - l + 1 < n. We define the beauty of a given subsegment as the value of the following expression:\max(a_{1}, a_{2}, \ldots, a_{l-1}, a_{r+1}, a_{r+2}, \ldots, a_{n}) - \min(a_{1}, a_{2}, \ldots, a_{l-1}, a_{r+1}, a_{r+2}, \ldots, a_{n}) + \max(a_{l}, \ldots, a_{r}) - \min(a_{l}, \ldots, a_{r}).Please find the maximum beauty among all proper subsegments.InputThe first line contains one integer t (1 \leq t \leq 1000) — the number of test cases. Then follow the descriptions of each test case.The first line of each test case contains a single integer n (4 \leq n \leq 10^5) — the length of the array.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 elements of the given array.It is guaranteed that the sum of n over all test cases does not exceed 10^5.OutputFor each testcase print a single integer — the maximum beauty of a proper subsegment.ExampleInput
4
8
1 2 2 3 1 5 6 1
5
1 2 3 100 200
4
3 3 3 3
6
7 8 3 1 1 8
Output
9
297
0
14
NoteIn the first test case, the optimal segment is l = 7, r = 8. The beauty of this segment equals to (6 - 1) + (5 - 1) = 9.In the second test case, the optimal segment is l = 2, r = 4. The beauty of this segment equals (100 - 2) + (200 - 1) = 297.
4
8
1 2 2 3 1 5 6 1
5
1 2 3 100 200
4
3 3 3 3
6
7 8 3 1 1 8

9 297 0 14 
['brute force', 'data structures', 'greedy', 'math', 'sortings', '*800']