D. Matryoshkastime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputMatryoshka 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.InputThe 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.OutputFor each test case, print one integer k — the minimum possible number of matryoshkas sets.ExampleInput
1062 2 3 4 3 1511 8 7 10 961000000000 1000000000 1000000000 1000000000 1000000000 100000000081 1 4 4 2 3 2 361 2 3 2 3 4710 11 11 12 12 13 1378 8 9 9 10 10 1184 14 5 15 6 16 7 1785 15 6 14 8 12 9 1154 2 2 3 4Output
2
1
6
2
2
2
2
2
4
3
NoteThe 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.
1062 2 3 4 3 1511 8 7 10 961000000000 1000000000 1000000000 1000000000 1000000000 100000000081 1 4 4 2 3 2 361 2 3 2 3 4710 11 11 12 12 13 1378 8 9 9 10 10 1184 14 5 15 6 16 7 1785 15 6 14 8 12 9 1154 2 2 3 4
2 1 6 2 2 2 2 2 4 3 
['data structures', 'greedy', 'sortings', '*1200']