#P1406A. Subset Mex
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ID: 5544
Type: RemoteJudge
1000ms
512MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Subset Mex
No submission language available for this problem.
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 $B$.
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.
For each test case, print the maximum value of $mex(A)+mex(B)$.
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 $mex(A)+mex(B)$.
Samples
4
6
0 2 1 5 0 1
3
0 1 2
4
0 2 0 1
6
1 2 3 4 5 6
5
3
4
0
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.