D. Jellyfish and Mextime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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. InputEach 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.OutputFor each test case, output a single integer — the minimum value of m if the operations are performed optimally.ExampleInput
485 2 1 0 3 0 4 021 251 0 2 114514 080 1 2 0 1 2 0 3Output
3
0
2
7
NoteIn 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.
485 2 1 0 3 0 4 021 251 0 2 114514 080 1 2 0 1 2 0 3
3 0 2 7 
['dp', '*1600']