Plus One on the Subset
Description
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.
Input
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 $a$.
Output
For each test case, print one integer — the minimum number of operations to make all elements of the array $a$ equal.
Samples
3
6
3 4 2 4 1 2
3
1000 1002 998
2
12 11
3
4
1
Note
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 $a=[12,12]$.