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.*;

public class Subsetmexdemo {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner sc =new Scanner(System.in);
        int t = sc.nextInt();
        for(int i = 0; i < t; i++){
            int n = sc.nextInt();
            Integer[] arr = new Integer[n];
            Set<Integer> set1 = new HashSet<>();
            Set<Integer> set2 = new HashSet<>();
            for(int j = 0; j < n; j ++){
                arr[j] = sc.nextInt();
                if(!set1.contains(arr[j])){
                    set1.add(arr[j]);
                }
                else{
                    set2.add(arr[j]);
                }
            }
            Object[] a = set1.toArray();
            Object[] b = set2.toArray();
            Arrays.sort(a);
            Arrays.sort(b);
            int output = 0, k = 0;
            
             
            for(k = 0; k < a.length; k++){
                if((int)a[k] != k){
                    output = k;
                    break;
                }
                
            }
            if(a.length == k){
                output = k;
            }
            for(k = 0; k < b.length; k++){
                if((int)b[k] != k){
                    output += k;
                    break;
                }
               
            }
            if(b.length == k){
                output += k;
            }
            System.out.println(output);
        }
        
    }
    
}