Plus One on the Subset

2000ms

262144K

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 $$$a_1=a_2=\dots=a_n$$$)?

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.

Sample Input:

3
6
3 4 2 4 1 2
3
1000 1002 998
2
12 11

Sample Output:

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 $$$a=[12,12]$$$.

Informação

Provedor Codeforces

Código CF1624A