A11294. Too Min Too Max

Given an array $a$ of $n$ elements, find the maximum value of the expression:

$$$$|a_i - a_j| + |a_j - a_k| + |a_k - a_l| + |a_l - a_i| $$ </p><p>where $i$ , $j$ , $k$ , and $l$ are four <span class="tex-font-style-bf">distinct</span> indices of the array $a$ , with $1 \\le i, j, k, l \\le n$ .</p><p>Here $|x|$ denotes the absolute value of $x$$$.

The first line contains one integer $t$ ( $1 \le t \le 500$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $n$ ( $4 \le n \le 100$ ) — the length of the given array.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $-10^6 \le a_i \le 10^6$ ).

For each test case, print a single integer — the maximum value.

In the first test case, for any selection of $i$ , $j$ , $k$ , $l$ , the answer will be $0$ . For example, $|a_1 - a_2| + |a_2 - a_3| + |a_3 - a_4| + |a_4 - a_1| = |1 - 1| + |1 - 1| + |1 - 1| + |1 - 1| = 0 + 0 + 0 + 0 = 0$ .

In the second test case, for $i = 1$ , $j = 3$ , $k = 2$ , and $l = 5$ , the answer will be $6$ . $|a_1 - a_3| + |a_3 - a_2| + |a_2 - a_5| + |a_5 - a_1| = |1 - 2| + |2 - 1| + |1 - 3| + |3 - 1| = 1 + 1 + 2 + 2 = 6$ .