Description

Input

Each test contains multiple test cases. The first line contains an integer $t$ ($1 \leq t \leq 2 \cdot 10^4$) — the number of test cases. The following lines contain the description of each test case.

The first line of each test case contains an integer $n$ ($3 \leq n \leq 2 \cdot 10^5$) — the number of bricks.

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 weights of the bricks.

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

Output

For each test case, output a line containing an integer representing the maximum possible final score if Pak Chanek distributes the bricks optimally.

3
5
3 1 5 2 3
4
17 8 19 45
8
265 265 265 265 265 265 265 265
 
 
 
 

6
63
0

Note

In the first test case, one way of achieving a final score of $6$ is to do the following:

• Put bricks $1$, $4$, and $5$ into bag $1$.
• Put brick $3$ into bag $2$.
• Put brick $2$ into bag $3$.

If Pak Chanek distributes the bricks that way, a way Bu Dengklek can take the bricks is:

• Take brick $5$ from bag $1$.
• Take brick $3$ from bag $2$.
• Take brick $2$ from bag $3$.

The score is $|a_5 - a_3| + |a_3 - a_2| = |3 - 5| + |5 - 1| = 6$. It can be shown that Bu Dengklek cannot get a smaller score from this distribution.

It can be shown that there is no other distribution that results in a final score bigger than $6$.