CF1543B Customising the Track

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.

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 $ .

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.

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.