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.io.*;
public class subset
{
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
        FastReader()
        {
            br=new BufferedReader(new InputStreamReader(System.in));
        }
        String next()
        {
            while(st==null||!st.hasMoreElements())
            {
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    e.printStackTrace();
                    //TODO: handle exception
                }
            }
            return st.nextToken();
        }
        int nextInt()
        {
            return Integer.parseInt(next());
        }
    }
    public static void main(String[] args) {
        FastReader sc=new FastReader();
        int t=sc.nextInt();
        int i=0,j=0;
        int mina=-1,minb=-1;
        int mid=0;
        int sizea[];
        int sizeb[];int k=0;
        while(t>0)
        {
            sizea=new int[101];
            sizeb=new int[101];
            mina=-1;
            minb=-1;
            k=0;
            t--;
            int n=sc.nextInt();
            int arr[]=new int[n];
            for(i=0;i<n;i++)
            {
                arr[i]=sc.nextInt();
            }
            if(n%2==0)
            {
                mid=n/2;
                for(j=0;j<mid;j++)
                {   
                    sizea[arr[j]]=1;
                    sizeb[arr[mid+j]]=1;
                }
                for(j=0;j<=mid+1;j++)
                {   
                   if(sizea[j]!=1&&mina==-1)
                    {
                       
                        if(sizeb[j]==1)
                        {
                            sizea[j]=1;
                            sizeb[j]=1;                            
                        }
                        else 
                       { mina=j;}
                    }
                    if(sizeb[j]!=1&&minb==-1)
                    {minb=j;}
                  
                }
            }
            else 
            {
                minb=0;
                for(j=0;j<n;j++)
                {   
                    sizea[arr[j]]=1;
                }
                for(j=0;j<=n+1;j++)
                {   
                   if(sizea[j]!=1&&mina==-1)
                    {mina=j;
                    break;}
                }
            }
            System.out.println(mina+minb);

        }
    }
}