CF1790D.Matryoshkas

Matryoshka is a wooden toy in the form of a painted doll, inside which you can put a similar doll of a smaller size.

A set of nesting dolls contains one or more nesting dolls, their sizes are consecutive positive integers. Thus, a set of nesting dolls is described by two numbers: $s$ — the size of a smallest nesting doll in a set and $m$ — the number of dolls in a set. In other words, the set contains sizes of $s, s + 1, \dots, s + m - 1$ for some integer $s$ and $m$ ($s,m \gt 0$).

You had one or more sets of nesting dolls. Recently, you found that someone mixed all your sets in one and recorded a sequence of doll sizes — integers $a_1, a_2, \dots, a_n$.

You do not remember how many sets you had, so you want to find the minimum number of sets that you could initially have.

For example, if a given sequence is $a=[2, 2, 3, 4, 3, 1]$. Initially, there could be $2$ sets:

• the first set consisting of $4$ nesting dolls with sizes $[1, 2, 3, 4]$;
• a second set consisting of $2$ nesting dolls with sizes $[2, 3]$.

According to a given sequence of sizes of nesting dolls $a_1, a_2, \dots, a_n$, determine the minimum number of nesting dolls that can make this sequence.

Each set is completely used, so all its nesting dolls are used. Each element of a given sequence must correspond to exactly one doll from some set.

套娃是一种木制玩具，外形为一个彩绘玩偶，其内部可嵌套一个尺寸更小的相似玩偶。

一套套娃包含一个或多个嵌套玩偶，它们的尺寸为连续的正整数。因此，一套套娃由两个数描述：$s$ —— 该套中最小玩偶的尺寸，以及 $m$ —— 该套中玩偶的总数。换言之，该套包含尺寸为 $s, s + 1, \dots, s + m - 1$ 的玩偶（其中 $s,m$ 为正整数）。

你原本拥有一套或多套这样的套娃。最近，你发现有人将你所有的套娃全部混在一起，并记录下了一串玩偶尺寸序列 —— 整数 $a_1, a_2, \dots, a_n$。

你不记得自己原先有多少套套娃，因此希望找出最初可能拥有的最少套数。

例如，若给定序列为 $a=[2, 2, 3, 4, 3, 1]$，则最初可能仅有 $2$ 套：

• 第一套包含 $4$ 个套娃，尺寸为 $[1, 2, 3, 4]$；
• 第二套包含 $2$ 个套娃，尺寸为 $[2, 3]$。

根据给定的套娃尺寸序列 $a_1, a_2, \dots, a_n$，确定能构成该序列的最少套娃套数。

每套必须被完全使用，即该套中所有玩偶均需出现在序列中；序列中的每个元素必须恰好对应某一套中一个玩偶。

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

The description of the test cases follows.

The first line of each test case contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the total number of matryoshkas that were in all sets.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$) — the sizes of the matryoshkas.

It is guaranteed that the sum of values of $n$ over all test cases does not exceed $2\cdot10^5$.

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

随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 2 \cdot 10^5$）—— 所有套娃集合中套娃的总数。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$1 \le a_i \le 10^9$）—— 各套娃的尺寸。

保证所有测试用例中 $n$ 的总和不超过 $2\cdot10^5$。

For each test case, print one integer $k$ — the minimum possible number of matryoshkas sets.

对于每个测试用例，输出一个整数 $k$ —— 即套娃集合的最少可能数量。

The first test case is described in the problem statement.

In the second test case, all matryoshkas could be part of the same set with minimum size $s=7$.

In the third test case, each matryoshka represents a separate set.

第一个测试用例已在题目描述中给出。

在第二个测试用例中，所有套娃均可组成一个集合，其最小尺寸为 $s=7$。

在第三个测试用例中，每个套娃各自构成一个独立的集合。