CF1720B.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 $r - l + 1 \lt n$. 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.

给你一个包含 $n$ 个整数的数组 $a$。你可以从中任选一个真子段 $a_l, a_{l + 1}, \ldots, a_r$，即任选两个整数 $1 \le l \le r \le n$，满足 $r - l + 1 \lt n$。我们定义该子段的美观度为如下表达式的值：

$$\max(a_{1}, a_{2}, \ldots, a_{l-1}, a_{r+1}, a_{r+2}, \ldots, a_{n}) - \min(a_{1}, a_{2}, \ldots, a_{l-1}, a_{r+1}, a_{r+2}, \ldots, a_{n}) + \max(a_{l}, \ldots, a_{r}) - \min(a_{l}, \ldots, a_{r}).$$

请找出所有真子段中的最大美观度。

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 $10^5$.

第一行包含一个整数 $t$（$1 \leq t \leq 1000$）—— 表示测试用例的数量。随后是每个测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$4 \leq n \leq 10^5$）—— 表示数组的长度。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$1 \leq a_{i} \leq 10^9$）—— 表示给定数组的元素。

保证所有测试用例的 $n$ 之和不超过 $10^5$。

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

对于每个测试用例，输出一个整数——合法子区间的最大美观度。

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 $(100 - 2) + (200 - 1) = 297$.

在第一个测试用例中，最优区间为 $l = 7$，$r = 8$。该区间的美丽值等于 $(6 - 1) + (5 - 1) = 9$。

在第二个测试用例中，最优区间为 $l = 2$，$r = 4$。该区间的美丽值等于 $(100 - 2) + (200 - 1) = 297$。