Subset Mex

1000ms

524288K

Description:

Given a set of integers (it can contain equal elements).

You have to split it into two subsets $$$A$$$ and $$$B$$$ (both of them can contain equal elements or be empty). You have to maximize the value of $$$mex(A)+mex(B)$$$.

Here $$$mex$$$ of a set denotes the smallest non-negative integer that doesn't exist in the set. For example:

$$$mex(\{1,4,0,2,2,1\})=3$$$
$$$mex(\{3,3,2,1,3,0,0\})=4$$$
$$$mex(\varnothing)=0$$$ ($$$mex$$$ for empty set)

The set is splitted into two subsets $$$A$$$ and $$$B$$$ if for any integer number $$$x$$$ the number of occurrences of $$$x$$$ into this set is equal to the sum of the number of occurrences of $$$x$$$ into $$$A$$$ and the number of occurrences of $$$x$$$ into $$$B$$$.

Input:

The input consists of multiple test cases. The first line contains an integer $$$t$$$ ($$$1\leq t\leq 100$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$1\leq n\leq 100$$$) — the size of the set.

The second line of each testcase contains $$$n$$$ integers $$$a_1,a_2,\dots a_n$$$ ($$$0\leq a_i\leq 100$$$) — the numbers in the set.

Output:

For each test case, print the maximum value of $$$mex(A)+mex(B)$$$.

Sample Input:

4
6
0 2 1 5 0 1
3
0 1 2
4
0 2 0 1
6
1 2 3 4 5 6

Sample Output:

Note:

In the first test case, $$$A=\left\{0,1,2\right\},B=\left\{0,1,5\right\}$$$ is a possible choice.

In the second test case, $$$A=\left\{0,1,2\right\},B=\varnothing$$$ is a possible choice.

In the third test case, $$$A=\left\{0,1,2\right\},B=\left\{0\right\}$$$ is a possible choice.

In the fourth test case, $$$A=\left\{1,3,5\right\},B=\left\{2,4,6\right\}$$$ is a possible choice.

Informação

Provedor Codeforces

Código CF1406A