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

Polycarp 收到了一个整数数组 $a[1 \dots n]$ 作为礼物。现在，他希望执行若干次（可能为零次）操作，使得数组中所有元素都相等（即满足 $a_1=a_2=\dots=a_n$）。

• 每次操作中，他可以选择数组中的若干下标，并将这些下标位置上的元素值增加 $1$。

例如，设 $a=[4,2,1,6,2]$。他可以执行如下操作：选择下标 $1$、$2$ 和 $4$，并将这些位置上的元素值各加 $1$。这样，一次操作后，数组变为 $a=[5,3,1,7,2]$。

为使数组中所有元素相等（即满足 $a_1=a_2=\dots=a_n$），所需的最少操作次数是多少？

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 $a$.

输入的第一行包含一个整数 $t$（$1 \le t \le 10^4$）——测试用例的数量。

接下来是各测试用例的输入描述。

每个测试用例描述的第一行包含一个整数 $n$（$1 \le n \le 50$）——数组 $a$ 的长度。

每个测试用例描述的第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$1 \le a_i \le 10^9$）——数组 $a$ 的元素。

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

对于每个测试用例，输出一个整数——使数组 $a$ 的所有元素相等所需的最少操作次数。

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 $a=[12,12]$.

第一个测试用例：

• $a=[3,4,2,4,1,2]$，选取 $a_3, a_5$ 并对它们执行加一操作，结果得到 $a=[3,4,3,4,2,2]$。
• $a=[3,4,3,4,2,2]$，选取 $a_1, a_5, a_6$ 并对它们执行加一操作，结果得到 $a=[4,4,3,4,3,3]$。
• $a=[4,4,3,4,3,3]$，选取 $a_3, a_5, a_6$ 并对它们执行加一操作，结果得到 $a=[4,4,4,4,4,4]$。

存在其他由 $3$ 次操作组成的序列，使得所有元素在操作后均相等。

第二个测试用例：

• $a=[1000,1002,998]$，选取 $a_1, a_3$ 并对其执行两次加一操作，结果得到 $a=[1002,1002,1000]$。
• $a=[1002,1002,1000]$，再对 $a_3$ 执行两次加一操作，结果得到 $a=[1002,1002,1002]$。

第三个测试用例：

• $a=[12,11]$，选取 $a_2$ 并对其执行一次加一操作，结果得到 $a=[12,12]$。