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 $$$c$$$.

Input

Each 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.

Output

For each test case, output the minimum score over all valid partitions.

Note

In 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 $$$\operatorname{mex} 0$$$.

Idx	Name	Rating
A	MEX Partition	800
B	Distinct Elements	1100
C	Reverse XOR	1300

Codeforces Round 1058 (Div. 2)