CF1734A.Select Three Sticks

You are given $n$ sticks with positive integral length $a_1, a_2, \ldots, a_n$.

You can perform the following operation any number of times (possibly zero):

• choose one stick, then either increase or decrease its length by $1$. After each operation, all sticks should have positive lengths.

What is the minimum number of operations that you have to perform such that it is possible to select three of the $n$ sticks and use them without breaking to form an equilateral triangle?

An equilateral triangle is a triangle where all of its three sides have the same length.

给你 $n$ 根长度为正整数的木棍，其长度分别为 $a_1, a_2, \ldots, a_n$。

你可以执行以下操作任意多次（包括零次）：

• 选择一根木棍，将其长度增加或减少 $1$。每次操作后，所有木棍的长度必须仍为正整数。

你需要执行的最少操作次数是多少，才能使得从这 $n$ 根木棍中选出三根，不折断地组成一个等边三角形？

等边三角形是指其三条边长度均相等的三角形。

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 $300$.

输入的第一行包含一个整数 $t$（$1 \le t \le 100$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$3 \le n \le 300$），表示木棍的数量。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$1 \le a_i \le 10^9$），表示各木棍的长度。

保证所有测试用例的 $n$ 值之和不超过 $300$。

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

对于每个测试用例，在一行中输出一个整数——所需执行的最少操作次数。

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.

在第一个测试用例中，你可以将第一根木棍的长度增加 $1$，然后将第三根木棍的长度减少 $1$。总共执行 $2$ 次操作，使得这三根木棍构成一个边长为 $2$ 的等边三角形。

在第四个测试用例中，你可以将第七根木棍的长度减少 $1$。此时可选取第二、第四和第七根木棍，构成一个边长为 $1$ 的等边三角形。