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 $$$1 \le i \lt j \le n$$$ 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.

Input

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 $$$2 \cdot 10^5$$$.

Output

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

Note

In the first test case, it is not possible to achieve a sum $$$ \gt 3$$$ 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 $$$ \gt 18$$$ by using these operations, therefore the maximum sum is $$$18$$$.

Another Array Problem

Examples