CF1615A.Closing The Gap

There are $n$ block towers in a row, where tower $i$ has a height of $a_i$. You're part of a building crew, and you want to make the buildings look as nice as possible. In a single day, you can perform the following operation:

• Choose two indices $i$ and $j$ ($1 \leq i, j \leq n$; $i \neq j$), and move a block from tower $i$ to tower $j$. This essentially decreases $a_i$ by $1$ and increases $a_j$ by $1$.

You think the ugliness of the buildings is the height difference between the tallest and shortest buildings. Formally, the ugliness is defined as $\max(a)-\min(a)$.

What's the minimum possible ugliness you can achieve, after any number of days?

一行中有 $n$ 座积木塔，其中第 $i$ 座塔的高度为 $a_i$。你是一名建筑队的成员，希望让这些建筑看起来尽可能美观。在一天内，你可以执行以下操作：

• 选择两个下标 $i$ 和 $j$（满足 $1 \leq i, j \leq n$ 且 $i \neq j$），并将一个积木块从第 $i$ 座塔移动到第 $j$ 座塔。该操作实质上使 $a_i$ 减少 $1$，同时使 $a_j$ 增加 $1$。

你认为建筑的“丑陋度”等于最高塔与最矮塔之间的高度差。形式化地，丑陋度定义为 $\max(a)-\min(a)$。

在经过任意天数的操作后，你能达到的最小可能丑陋度是多少？

The first line contains one integer $t$ ($1 \leq t \leq 1000$) — the number of test cases. Then $t$ cases follow.

The first line of each test case contains one integer $n$ ($2 \leq n \leq 100$) — the number of buildings.

The second line of each test case contains $n$ space separated integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 10^7$) — the heights of the buildings.

第一行包含一个整数 $t$（$1 \leq t \leq 1000$），表示测试用例的数量。随后是 $t$ 个测试用例。

每个测试用例的第一行包含一个整数 $n$（$2 \leq n \leq 100$），表示建筑物的数量。

每个测试用例的第二行包含 $n$ 个以空格分隔的整数 $a_1, a_2, \ldots, a_n$（$1 \leq a_i \leq 10^7$），表示各建筑物的高度。

For each test case, output a single integer — the minimum possible ugliness of the buildings.

对于每个测试用例，输出一个整数——建筑物的最小可能丑陋度。

In the first test case, the ugliness is already $0$.

In the second test case, you should do one operation, with $i = 1$ and $j = 3$. The new heights will now be $[2, 2, 2, 2]$, with an ugliness of $0$.

In the third test case, you may do three operations:

1. with $i = 3$ and $j = 1$. The new array will now be $[2, 2, 2, 1, 5]$,
2. with $i = 5$ and $j = 4$. The new array will now be $[2, 2, 2, 2, 4]$,
3. with $i = 5$ and $j = 3$. The new array will now be $[2, 2, 3, 2, 3]$.

The resulting ugliness is $1$. It can be proven that this is the minimum possible ugliness for this test.

在第一个测试用例中，丑陋度已经是 $0$。

在第二个测试用例中，你需要执行一次操作，其中 $i = 1$ 且 $j = 3$。新的高度数组将变为 $[2, 2, 2, 2]$，丑陋度为 $0$。

在第三个测试用例中，你可以执行三次操作：

1. 取 $i = 3$ 且 $j = 1$，新数组变为 $[2, 2, 2, 1, 5]$；
2. 取 $i = 5$ 且 $j = 4$，新数组变为 $[2, 2, 2, 2, 4]$；
3. 取 $i = 5$ 且 $j = 3$，新数组变为 $[2, 2, 3, 2, 3]$。

最终的丑陋度为 $1$。可以证明，这是该测试用例所能达到的最小丑陋度。