A14696 | 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?

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.

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