B. Customising the Tracktime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputHighway 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.InputThe 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.OutputFor 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.ExampleInput
3
3
1 2 3
4
0 1 1 0
10
8 3 6 11 5 2 1 7 10 4
Output
0
4
21
NoteFor 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.
3
3
1 2 3
4
0 1 1 0
10
8 3 6 11 5 2 1 7 10 4

0 4 21 
['combinatorics', 'greedy', 'math', '*900']