CF2130A Submission is All You Need

For a multiset $ T $ consisting of non-negative integers, we define: - $ \text{sum}(T) $ is the sum of all elements in $ T $ . For example, if $ T = \{0,1, 1, 3\} $ , then $ \text{sum}(T)= 0+1+1+3=5 $ . - $ \text{mex}(T) $ is the smallest non-negative integer not in $ T $ . For example, if $ T = \{0,1, 1, 3\} $ , then $ \text{mex}(T) = 2 $ because $ 2 $ is the smallest non-negative integer not present in $ T $ . You are given a multiset $ S $ of size $ n $ consisting of non-negative integers. At first, your score is $ 0 $ . You can perform the following operations any number of times in any order (possibly zero):- Select a subset $ S' \subseteq S $ (i.e., $ S' $ contains some of the elements currently in $ S $ ), add $ \text{sum}(S') $ to your score, and then remove $ S' $ from $ S $ . - Select a subset $ S' \subseteq S $ , add $ \text{mex}(S') $ to your score, and then remove $ S' $ from $ S $ . Find the maximum possible score that can be obtained.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^3 $ ). The description of the test cases follows. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 50 $ ). The second line of each test case contains $ n $ integers $ S_1, S_2, \ldots, S_n $ ( $ 0 \le S_i \le 50 $ ).

For each test case, print a single integer — the maximum possible score that can be obtained.

In the first test case, a possible optimal strategy is as follows: - Select $ S'=\{0,1\} $ , add $ \text{mex}(S')=\text{mex}(\{0,1\})=2 $ to your score, and then remove $ S' $ from $ S $ . Currently, your score is $ 2 $ and $ S=\{1\} $ . - Select $ S'=\{1\} $ , add $ \text{sum}(S')=\text{sum}(\{1\})=1 $ to your score, and then remove $ S' $ from $ S $ . Currently, your score is $ 3 $ and $ S=\varnothing $ . After that, you cannot do any further operations. It can be proven that $ 3 $ is the maximum possible score that can be obtained.