Customising the Track

题意翻译

给定整数 $n$ 和长度为 $n$ 的序列 $a$，你可以进行下列操作任意次： - 选择整数 $i,j$ 满足 $1\leq i,j\leq n$ 且 $a_i>0$，使 $a_i$ 减一，$a_j$ 加一。 求出操作后 $\sum\limits_{i=1}^n\sum\limits_{j=i+1}^n|a_i-a_j|$ 的最小值。$T$ 组数据。 $1\leq T\leq10^4;1\leq n,\sum n\leq2\times10^5;0\leq a_i\leq10^9;$

题目描述

Highway 201 is the most busy street in Rockport. Traffic cars cause a lot of hindrances to races, especially when there are a lot of them. The track which passes through this highway can be divided into $ n $ sub-tracks. You are given an array $ a $ where $ a_i $ represents the number of traffic cars in the $ i $ -th sub-track. You define the inconvenience of the track as $ \sum\limits_{i=1}^{n} \sum\limits_{j=i+1}^{n} \lvert a_i-a_j\rvert $ , where $ |x| $ is the absolute value of $ x $ . You can perform the following operation any (possibly zero) number of times: choose a traffic car and move it from its current sub-track to any other sub-track. Find the minimum inconvenience you can achieve.

输入输出格式

输入格式

The first line of input contains a single integer $ t $ ( $ 1\leq t\leq 10\,000 $ ) — the number of test cases. The first line of each test case contains a single integer $ n $ ( $ 1\leq n\leq 2\cdot 10^5 $ ). The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 0\leq a_i\leq 10^9 $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2\cdot 10^5 $ .

输出格式

For each test case, print a single line containing a single integer: the minimum inconvenience you can achieve by applying the given operation any (possibly zero) number of times.

输入输出样例

输入样例 #1

3
3
1 2 3
4
0 1 1 0
10
8 3 6 11 5 2 1 7 10 4

输出样例 #1

0
4
21

说明

For the first test case, you can move a car from the $ 3 $ -rd sub-track to the $ 1 $ -st sub-track to obtain $ 0 $ inconvenience. For the second test case, moving any car won't decrease the inconvenience of the track.