CF1624A.Plus One on the Subset

Polycarp got an array of integers $a[1 \dots n]$ as a gift. Now he wants to perform a certain number of operations (possibly zero) so that all elements of the array become the same (that is, to become $a_1=a_2=\dots=a_n$ ).

• In one operation, he can take some indices in the array and increase the elements of the array at those indices by $1$ .

For example, let $a=[4,2,1,6,2]$ . He can perform the following operation: select indices 1, 2, and 4 and increase elements of the array in those indices by $1$ . As a result, in one operation, he can get a new state of the array $a=[5,3,1,7,2]$ .

What is the minimum number of operations it can take so that all elements of the array become equal to each other (that is, to become $a_1=a_2=\dots=a_n$ )?

The first line of the input contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases in the test.

The following are descriptions of the input test cases.

The first line of the description of each test case contains one integer $n$ ( $1 \le n \le 50$ ) — the array $a$ .

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

For each test case, print one integer — the minimum number of operations to make all elements of the array $a$ equal.

First test case:

• $a=[3,4,2,4,1,2]$ take $a_3, a_5$ and perform an operation plus one on them, as a result we get $a=[3,4,3,4,2,2]$ .
• $a=[3,4,3,4,2,2]$ we take $a_1, a_5, a_6$ and perform an operation on them plus one, as a result we get $a=[4,4,3,4,3,3]$ .
• $a=[4,4,3,4,3,3]$ we take $a_3, a_5, a_6$ and perform an operation on them plus one, as a result we get $a=[4,4,4,4,4,4]$ .

There are other sequences of $3$ operations, after the application of which all elements become equal.

Second test case:

• $a=[1000,1002,998]$ 2 times we take $a_1, a_3$ and perform an operation plus one on them, as a result we get $a=[1002,1002,1000]$ .
• $a=[1002,1002,1000]$ also take $a_3$ 2 times and perform an operation plus one on it, as a result we get $a=[1002,1002,1002]$ .

Third test case:

• $a=[12,11]$ take $a_2$ and perform an operation plus one on it, as a result we get $a=[12,12]$ .