write a go solution for Description:
You 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<=l<=r<=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.

Input Format:
The first line contains one integer t (1<=t<=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<=n<=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<=a_i<=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.

Output Format:
For each testcase print a single integer — the maximum beauty of a proper subsegment.

Note:
In 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.. Output only the code with no comments, explanation, or additional text.