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

public class A
{
   public static void main(String[] args) throws IOException
   {
      BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
      PrintWriter out = new PrintWriter(System.out);
      int T = Integer.parseInt(br.readLine());
      for(int t = 0; t < T; t++){
         int N = Integer.parseInt(br.readLine());
         StringTokenizer st = new StringTokenizer(br.readLine());
         int[] arr = new int[N];
         for(int i = 0; i < N; i++){
            arr[i] = Integer.parseInt(st.nextToken());
         }
         Arrays.sort(arr);
         int ac = 0; int bc = 0;
         ArrayList<Integer> alist = new ArrayList<Integer>();
         ArrayList<Integer> blist = new ArrayList<Integer>();
         int i = 0;
         int count = 0;
         while(i < N && arr[i] == 0){
            count++;
            i++;
         }
         if(count >= 2){
            ac++; bc++;
            alist.add(0);
            blist.add(0);
         }
         else if(count == 1){
            ac++;
            alist.add(0);
         }
         boolean flaga = true;
         boolean flagb = true;
         for(; i < N; i++){
            if(ac == 0){
               continue;
            }
            if(alist.isEmpty() || alist.get(alist.size()-1) < arr[i]){
               if((arr[i] == alist.get(alist.size()-1) + 1) && flaga){
                  ac++;
                  alist.add(arr[i]);
               }
               else{
                  flaga = false;
               }
            }
            else{
               if(bc == 0){
                  continue;
               }
               if((arr[i] == blist.get(blist.size()-1) + 1) && flagb){
                  bc++;
                  blist.add(arr[i]);
               }
               else{
                  flagb = false;
               }
            }
         }
         out.println(ac + bc);
      }
      out.close();
   }
}