CF1607C.Minimum Extraction

Yelisey has an array $a$ of $n$ integers.

If $a$ has length strictly greater than $1$, then Yelisei can apply an operation called minimum extraction to it:

1. First, Yelisei finds the minimal number $m$ in the array. If there are several identical minima, Yelisey can choose any of them.
2. Then the selected minimal element is removed from the array. After that, $m$ is subtracted from each remaining element.

Thus, after each operation, the length of the array is reduced by $1$.

For example, if $a = [1, 6, -4, -2, -4]$, then the minimum element in it is $a_3 = -4$, which means that after this operation the array will be equal to $a=[1 {- (-4)}, 6 {- (-4)}, -2 {- (-4)}, -4 {- (-4)}] = [5, 10, 2, 0]$.

Since Yelisey likes big numbers, he wants the numbers in the array $a$ to be as big as possible.

Formally speaking, he wants to make the minimum of the numbers in array $a$ to be maximal possible (i.e. he want to maximize a minimum). To do this, Yelisey can apply the minimum extraction operation to the array as many times as he wants (possibly, zero). Note that the operation cannot be applied to an array of length $1$.

Help him find what maximal value can the minimal element of the array have after applying several (possibly, zero) minimum extraction operations to the array.

叶列谢有一个包含 $n$ 个整数的数组 $a$。

若 $a$ 的长度严格大于 $1$，则叶列谢可以对其执行一种称为“最小值提取”的操作：

1. 首先，叶列谢找出数组中的最小数 $m$。若存在多个相同的最小值，叶列谢可任选其一。
2. 然后，将所选的最小元素从数组中移除；接着，将 $m$ 从每个剩余元素中减去。

因此，每次操作后，数组长度减少 $1$。

例如，若 $a = [1, 6, -4, -2, -4]$，则其中最小元素为 $a_3 = -4$，于是该操作后数组变为 $a=[1 {- (-4)}, 6 {- (-4)}, -2 {- (-4)}, -4 {- (-4)}] = [5, 10, 2, 0]$。

由于叶列谢喜欢较大的数，他希望数组 $a$ 中的数尽可能大。

形式化地说，他希望使数组 $a$ 中各数的最小值尽可能大（即最大化该最小值）。为此，叶列谢可以对数组执行任意多次（包括零次）最小值提取操作。注意：该操作不能在长度为 $1$ 的数组上执行。

请帮助他求出：对数组执行若干次（可能为零次）最小值提取操作后，数组中最小元素所能达到的最大值。

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

The next $2t$ lines contain descriptions of the test cases.

In the description of each test case, the first line contains an integer $n$ ($1 \leq n \leq 2 \cdot 10^5$) — the original length of the array $a$. The second line of the description lists $n$ space-separated integers $a_i$ ($-10^9 \leq a_i \leq 10^9$) — elements of the array $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

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

接下来的 $2t$ 行包含各测试用例的描述。

在每个测试用例的描述中，第一行包含一个整数 $n$（$1 \leq n \leq 2 \cdot 10^5$）—— 数组 $a$ 的原始长度。描述的第二行包含 $n$ 个以空格分隔的整数 $a_i$（$-10^9 \leq a_i \leq 10^9$）—— 数组 $a$ 的元素。

保证所有测试用例的 $n$ 之和不超过 $2 \cdot 10^5$。

Print $t$ lines, each of them containing the answer to the corresponding test case. The answer to the test case is a single integer — the maximal possible minimum in $a$, which can be obtained by several applications of the described operation to it.

输出 $t$ 行，每行包含对应测试用例的答案。每个测试用例的答案是一个整数——即通过对数组 $a$ 多次应用上述操作所能得到的最大可能的最小值。

In the first example test case, the original length of the array $n = 1$. Therefore minimum extraction cannot be applied to it. Thus, the array remains unchanged and the answer is $a_1 = 10$.

In the second set of input data, the array will always consist only of zeros.

In the third set, the array will be changing as follows: $[\color{blue}{-1}, 2, 0] \to [3, \color{blue}{1}] \to [\color{blue}{2}]$. The minimum elements are highlighted with $\color{blue}{\text{blue}}$. The maximal one is $2$.

In the fourth set, the array will be modified as $[2, 10, \color{blue}{1}, 7] \to [\color{blue}{1}, 9, 6] \to [8, \color{blue}{5}] \to [\color{blue}{3}]$. Similarly, the maximum of the minimum elements is $5$.

在第一个样例测试用例中，数组的原始长度为 $n = 1$。因此无法应用最小值提取操作。于是数组保持不变，答案为 $a_1 = 10$。

在第二组输入数据中，数组将始终仅由零组成。

在第三组中，数组的变化过程如下：$[\color{blue}{-1}, 2, 0] \to [3, \color{blue}{1}] \to [\color{blue}{2}]$。被标为 $\color{blue}{\text{蓝色}}$ 的元素为每次操作中被提取的最小元素。这些最小元素中的最大值为 $2$。

在第四组中，数组的变化过程为 $[2, 10, \color{blue}{1}, 7] \to [\color{blue}{1}, 9, 6] \to [8, \color{blue}{5}] \to [\color{blue}{3}]$。类似地，所有被提取的最小元素中的最大值为 $5$。