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.

201号公路是罗克波特市最繁忙的街道。过往车辆给比赛带来了诸多阻碍，尤其是当车流量很大时。穿过该公路的赛道可分为 $n$ 段子赛道。现给出一个数组 $a$，其中 $a_i$ 表示第 $i$ 段子赛道上的车辆数。我们定义该赛道的“不便度”为 $\sum\limits_{i=1}^{n} \sum\limits_{j=i+1}^{n} \lvert a_i-a_j\rvert$，其中 $|x|$ 表示 $x$ 的绝对值。

你可以执行以下操作任意次（包括零次）：任选一辆车，将其从当前子赛道移动到任意其他子赛道。

求你能达到的最小不便度。

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 $2\cdot 10^5$.

输入的第一行包含一个整数 $t$（$1\leq t\leq 10\,000$），表示测试用例的数量。

每个测试用例的第一行包含一个整数 $n$（$1\leq n\leq 2\cdot 10^5$）。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$0\leq a_i\leq 10^9$）。

保证所有测试用例的 $n$ 之和不超过 $2\cdot 10^5$。

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.

对于每个测试用例，输出一行，包含一个整数：通过任意（可能为零）次执行给定操作所能达到的最小不便度。

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.

对于第一个测试用例，你可以将一辆车从第 $3$ 条子轨道移动到第 $1$ 条子轨道，从而使得不便度为 $0$。

对于第二个测试用例，移动任意一辆车都无法降低轨道的不便度。