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 $$$1 \le l \le r \le n$$$, where $$$r - l + 1 < n$$$. We define the beauty of a given subsegment as the value of the following expression:
$$$$$$\max(a_{1}, a_{2}, \ldots, a_{l-1}, a_{r+1}, a_{r+2}, \ldots, a_{n}) - \min(a_{1}, a_{2}, \ldots, a_{l-1}, a_{r+1}, a_{r+2}, \ldots, a_{n}) + \max(a_{l}, \ldots, a_{r}) - \min(a_{l}, \ldots, a_{r}).$$$$$$
Please find the maximum beauty among all proper subsegments.
Input Format:
The first line contains one integer $$$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$$$.
Output Format:
For each testcase print a single integer — the maximum beauty of a proper subsegment.
Note:
In the first test case, the optimal segment is $$$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$$$.