CF2236A.Games on the Train

Dabir, Egor, and Arseniy just got on the train and decided to play a game. Dabir has a backpack with an infinite number of cubes. He built $n$ towers from them, where the $i$-th tower has height $h_i$ cubes.

Egor and Arseniy must choose an integer $x_i$ for each tower $i$ and increase its height by $x_i$ exactly once. For example, if $h$ = [$1, 3, 2, 2$], $x$ = [$3, 2, 2, 8$], then after increasing $h$ it will become [$4, 5, 4, 10$]. Their goal is to make the heights of all towers equal.

To make the game more interesting, Dabir wants to choose an integer $k$ and add a restriction: each $x_i$ must satisfy $1 \le x_i \le k$. Help him find the smallest $k$ for which it is possible to finish the game.

达比尔、叶戈尔和阿尔谢尼刚刚上了一列火车，决定玩一个游戏。达比尔的背包里有无限多个立方体，他用它们搭建了 $n$ 座塔，其中第 $i$ 座塔的高度为 $h_i$ 个立方体。

叶戈尔和阿尔谢尼必须为每座塔 $i$ 选择一个整数 $x_i$，并对该塔的高度恰好增加一次 $x_i$。例如，若 $h = [1, 3, 2, 2]$，$x = [3, 2, 2, 8]$，则增加后 $h$ 将变为 $[4, 5, 4, 10]$。他们的目标是使所有塔的高度相等。

为了使游戏更有趣，达比尔希望选择一个整数 $k$，并添加一条限制：每个 $x_i$ 必须满足 $1 \le x_i \le k$。请帮助他找出能够完成该游戏的最小 $k$。

The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

Then $t$ test cases follow.

The first line of each test case contains a single integer $n$ ($1 \le n \le 5$).

The second line contains $n$ integers $h_1, h_2, \dots, h_n$ ($1 \le h_i \le 6$).

第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 测试用例的数量。

接下来是 $t$ 个测试用例。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 5$）。

第二行包含 $n$ 个整数 $h_1, h_2, \dots, h_n$（$1 \le h_i \le 6$）。

For each test case, output a single integer — the minimum value of $k$ such that it is possible to make all towers have equal height.

对于每个测试用例，输出一个整数——使得所有塔的高度相等所需的最小 $k$ 值。

null