Select Three Sticks

Description:

Input:

The first line of the input contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$3 \le n \le 300$$$) — the number of sticks.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the lengths of the sticks.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$300$$$.

Output:

For each test case, print one integer on a single line — the minimum number of operations to be made.

Sample Input:

4
3
1 2 3
4
7 3 7 3
5
3 4 2 1 1
8
3 1 4 1 5 9 2 6

Sample Output:

2
4
1
1

Note:

In the first test case, you can increase the length of the first stick by $$$1$$$, then decrease the length of the third stick by $$$1$$$. In total, you perform $$$2$$$ operations, such that the three sticks form an equilateral triangle of side length $$$2$$$.

In the fourth test case, you can decrease the length of the seventh stick by $$$1$$$. An equilateral triangle of side length $$$1$$$ can be selected and formed by the second, fourth, and seventh sticks.