CF1406A 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) $ .

In the first test case, $ A=\left\{0,1,2\right\},B=\left\{0,1,5\right\} $ is a possible choice. In the second test case, $ A=\left\{0,1,2\right\},B=\varnothing $ is a possible choice. In the third test case, $ A=\left\{0,1,2\right\},B=\left\{0\right\} $ is a possible choice. In the fourth test case, $ A=\left\{1,3,5\right\},B=\left\{2,4,6\right\} $ is a possible choice.