Another Array Problem

题意翻译

你有一个长度为 $n$ 的数组 $a$, 你可以对它进行以下操作任意多次： - 选择两个下标 $i, j$, 满足 $1\leq i<j\leq n$, 将 $a_i \sim a_j$ 之间的所有元素替换成 $|a_i-a_j|$。 求数组能经过若干次操作以后达到的所有元素的最大和。 数据范围：$2\leq n, \sum n\leq 2\times 10^5, 1\leq a_ i\leq 10^9$。 Translated by Microchip2333.

题目描述

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.

输入输出格式

输入格式

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 $ .

输出格式

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

输入输出样例

输入样例 #1

3
3
1 1 1
2
9 1
3
4 9 5

输出样例 #1

3
16
18

说明

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 $ .