A15321 | Interesting Sum

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.