Interesting Sum
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.
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 $10^5$.
For each testcase print a single integer — the maximum beauty of a proper subsegment.
Input
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
For each testcase print a single integer — the maximum beauty of a proper subsegment.
Samples
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
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 $(100 - 2) + (200 - 1) = 297$.