Sasha decided to give his girlfriend an array $a_1, a_2, \ldots, a_n$. He found out that his girlfriend evaluates the beauty of the array as the sum of the values $(a_i - a_{i - 1})$ for all integers $i$ from $2$ to $n$.

Help Sasha and tell him the maximum beauty of the array $a$ that he can obtain, if he can rearrange its elements in any way.

Input

Each test consists of multiple test cases. The first line contains a single 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 $n$ ($2 \leq n \leq 100$) — the length of the array $a$.

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 elements of the array $a$.

Output

For each test case, output a single integer — the maximum beauty of the array $a$ that can be obtained.

Note

In the first test case, the elements of the array $a$ can be rearranged to make $a = [1, 2, 3]$. Then its beauty will be equal to $(a_2 - a_1) + (a_3 - a_2) = (2 - 1) + (3 - 2) = 2$.

In the second test case, there is no need to rearrange the elements of the array $a$. Then its beauty will be equal to $0$.

Samples

5
3
2 1 3
3
69 69 69
5
100 54 80 43 90
4
3 4 3 3
2
2 1

2
0
57
1
1