A13712 | Subset Mex

Given a set of integers (it can contain equal elements).

You have to split it into two subsets $A$ and $B$ (both of them can contain equal elements or be empty). You have to maximize the value of $mex(A)+mex(B)$ .

Here $mex$ of a set denotes the smallest non-negative integer that doesn't exist in the set. For example:

- $mex(\{1,4,0,2,2,1\})=3$
- $mex(\{3,3,2,1,3,0,0\})=4$
- $mex(\varnothing)=0$ ( $mex$ for empty set)

The set is splitted into two subsets $A$ and $B$ if for any integer number $x$ the number of occurrences of $x$ into this set is equal to the sum of the number of occurrences of $x$ into $A$ and the number of occurrences of $x$ into $B$ .

The input consists of multiple test cases. The first line contains an integer $t$ ( $1\leq t\leq 100$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $n$ ( $1\leq n\leq 100$ ) — the size of the set.

The second line of each testcase contains $n$ integers $a_1,a_2,\dots a_n$ ( $0\leq a_i\leq 100$ ) — the numbers in the set.

For each test case, print the maximum value of $mex(A)+mex(B)$ .