Plus One on the Subset

题意翻译

有一个长度为 $n$ 数列 $a$。定义一次操作如下： * 在 $a$ 中选出若干个数； * 将这些数 $+1$，并放回原处。 求至少经过多少次操作后，$a$ 数组中所有数一样。

题目描述

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 $ )?

输入输出格式

输入格式

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 $ .

输出格式

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

输入输出样例

输入样例 #1

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

输出样例 #1

3
4
1

说明

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] $ .