A14457. 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.