A15713 | 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 $m$ ( $s,m > 0$ ).

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.

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 $2\cdot10^5$ .

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