CF1875D Jellyfish and Mex

You are given an array of $ n $ nonnegative integers $ a_1, a_2, \dots, a_n $ . Let $ m $ be a variable that is initialized to $ 0 $ , Jellyfish will perform the following operation $ n $ times: - select an index $ i $ ( $ 1 \leq i \leq |a| $ ) and delete $ a_i $ from $ a $ . - add $ \operatorname{MEX}(a)^{\dagger} $ to $ m $ . Now Jellyfish wants to know the minimum possible final value of $ m $ if he performs all the operations optimally. $ ^{\dagger} $ The MEX (minimum excluded) of an array is the smallest non-negative integer that does not belong to the array. For instance: - The MEX of $ [2,2,1] $ is $ 0 $ , because $ 0 $ does not belong to the array. - The MEX of $ [3,1,0,1] $ is $ 2 $ , because $ 0 $ and $ 1 $ belong to the array, but $ 2 $ does not. - The MEX of $ [0,3,1,2] $ is $ 4 $ because $ 0 $ , $ 1 $ , $ 2 $ , and $ 3 $ belong to the array, but $ 4 $ does not.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \leq t \leq 5000 $ ). The description of the test cases follows. The first line of each test case contains a single integer $ n $ ( $ 1 \leq n \leq 5000 $ ) — the size of the array. The second line of each test case contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 0 \leq a_i \leq 10^9 $ ) — the integers in the array. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 5000 $ .

For each test case, output a single integer — the minimum value of $ m $ if the operations are performed optimally.

In the first test case, we delete elements from $ a $ in the following order: $ [5,2,\color{red}{1},0,3,0,4,0] \to [5,2,0,3,\color{red}{0},4,0] \to [5,2,\color{red}{0},3,4,0] \to [5,2,3,4,\color{red}{0}] \to [5,2,\color{red}{3},4] \to [\color{red}{5},2,4] \to [\color{red}{2},4] \to [\color{red}{4}] \to [~] $ . The value of $ m $ will be $ 1+1+1+0+0+0+0+0=3 $ .