A. MEX Partitiontime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard output Let a partition of a multiset $$$B$$$ be a collection of multisets $$$s_1, s_2,\ldots, s_k$$$ such that each element appears the same number of times in $$$B$$$ and across all of $$$s_1,s_2,\ldots,s_k$$$.For example, some partitions of $$$\{1,2,3,3\}$$$ include $$$\{1,3\}+\{2,3\}, \{1,2,3,3\}$$$, and $$$\{2\}+\{1,3\}+\{3\}$$$, but not $$$\{1,2\}+\{3\}$$$. A partition is called valid if the $$$\operatorname{mex}$$$$$$^{\text{∗}}$$$ of all multisets in the partition is the same. The score of a valid partition is the $$$\operatorname{mex}$$$ of any multiset in the partition.You are given a multiset $$$A$$$ of size $$$n$$$. Find the minimum score over all valid partitions of $$$A$$$.$$$^{\text{∗}}$$$The minimum excluded (MEX) of a collection of integers $$$c_1, c_2, \ldots, c_k$$$ is defined as the smallest non-negative integer $$$x$$$ which does not occur in the collection $$$c$$$. InputEach test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 100$$$). The description of the test cases follows. The first line of each test case contains an integer $$$n$$$ ($$$1 \leq n \leq 100$$$).The second line contains $$$n$$$ integers $$$A_1, A_2, \ldots, A_n$$$ denoting the elements of $$$A$$$ ($$$0 \leq A_i \leq 100$$$).It is not guaranteed that the elements are given in non-decreasing order.OutputFor each test case, output the minimum score over all valid partitions.ExampleInput230 0 021 2Output10NoteIn the first test case, the minimum score of $$$1$$$ can be obtained by the partition $$$\{0\}+\{0\}+\{0\}$$$. The partition is valid because each multiset has a $$$\operatorname{mex}$$$ of $$$1$$$, which is consequently the score of the partition.In the second test case, we can use $$$\{1,2\}$$$ as the only multiset in the partition, which has $$$\operatorname{mex} 0$$$.