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(∅)=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≤ t≤ 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≤ n≤ 100) — the size of the set.

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

Output

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

Example

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


Output


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=∅ 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.
1
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
 15
1
0
1
1
2
0 0
2
0 1
2
1 1
2
0 2
2
1 2
3
0 0 0
3
0 1 0
3
0 1 2
4
0 1 2 3
4
1 1 2 3
4
0 1 0 1
4
0 0 0 1
5
0 0 0 0 0

100
 1
0
2
2
0
1
0
2
3
3
4
0
4
3
2

import java.util.*; 
import java.lang.*; 
import java.io.*;

public class first {
PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
BufferedReader in = new BufferedReader(new InputStreamReader(System.in)); StringTokenizer tok;
    public int gcd(int a,int b)
    {
    	if(b==0) return a;
    	return gcd(b,a%b);
    }
	public void go() throws IOException
	{
			String test = in.readLine(); 
			if(test==null || test.trim().length()==0 )
				return ;
			
			tok = new StringTokenizer(test);
			int tt = Integer.parseInt(tok.nextToken()); 
			
			
			for (int t = 0; t < tt; t++)
			{ ntok();
				int n=ipar();
				ntok();
			  int a[]=iapar(n);
			  int max=-1;
			  HashMap<Integer,Integer> m=new HashMap<>();
			  for(int i=0;i<n;i++)
			  {  max=Math.max(max, a[i]);
				  m.put(a[i], m.getOrDefault(a[i], 0)+1);
			  }
			 // ArrayList<Integer> arr=new ArrayList<Integer>(m.keySet());
			  int ans1=0,ans2=0;
			  boolean isone=false;
			  //boolean absent=false;
			  for(int i=0;i<=max+1;i++) {
				  if(!m.containsKey(i))
				  {
					 ans2=i;break;
				  }
				  else
				  {
					  if(m.get(i)==1 && isone==false)
						  {ans1=i;
						   isone=true;
						  }
				  }
			  }
			  System.out.println(ans1+ans2);
			   
					
			}
			out.flush();
			in.close(); 
	}
	
	public void ntok() throws IOException
		{ String test = in.readLine(); 
			if(test==null || test.trim().length()==0 )
				return ;
			tok = new StringTokenizer(test);
	}
	
	public int ipar()
	{ 
		String test=tok.nextToken();
		if(test==null || test.trim().length()==0) 
			return 0;
		return Integer.parseInt(test); 
	}
	
	public int[] iapar(int n) 
	{
		int[] arr = new int[n]; 
		for (int i = 0; i < n; i++) 
		{
			arr[i] = ipar(); 
		}
		return arr; 
	}
	
	
	public long lpar()
	{ 	
		String test=tok.nextToken();
	
		if(test==null || test.trim().length()==0) 
			return 0;
		return Long.parseLong(test); 
	}
	
	public long[] lapar(int n) 
	{
		long[] arr = new long[n]; 
		
		for (int i = 0; i < n; i++)
		{
	        arr[i] = lpar(); 
		}
		return arr; 
	}

	public double dpar() 
	{
		return Double.parseDouble(tok.nextToken());
	}
	
	public String spar()
		{ 	String test=tok.nextToken();
			if(test==null || test.trim().length()==0) 
				return "";
			
			return test;
		}
	
	public static void main(String[] args) throws IOException
	{
		new first().go(); 
	}
}