CF1763C.Another Array Problem

You are given an array $a$ of $n$ integers. You are allowed to perform the following operation on it as many times as you want (0 or more times):

• Choose $2$ indices $i$ , $j$ where $1 \le i < j \le n$ and replace $a_k$ for all $i \leq k \leq j$ with $|a_i - a_j|$

Print the maximum sum of all the elements of the final array that you can obtain in such a way.

The first line contains a single integer $t$ ( $1 \le t \le 10^5$ ) — the number of test cases.

The first line of each test case contains a single integer $n$ ( $2 \le n \le 2 \cdot 10^5$ ) — the length of the array $a$ .

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le 10^9$ ) — the elements of array $a$ .

It's guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

For each test case, print the sum of the final array.

In the first test case, it is not possible to achieve a sum $> 3$ by using these operations, therefore the maximum sum is $3$ .

In the second test case, it can be shown that the maximum sum achievable is $16$ . By using operation $(1,2)$ we transform the array from $[9,1]$ into $[8,8]$ , thus the sum of the final array is $16$ .

In the third test case, it can be shown that it is not possible to achieve a sum $> 18$ by using these operations, therefore the maximum sum is $18$ .