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 GreedyMex {
	public static void main(String[] args) {
		Scanner sc  = new Scanner(System.in); 
		int t = sc.nextInt(); 
		for(int x = 0 ; x<t ; x++)
		{
			int n = sc.nextInt(); 
			
			int[] arr = new int[n]; 
			int [] freq = new int [n+1];
			for(int j = 0 ; j < n ; j++)
			{
				arr[j] = sc.nextInt();
				if(arr[j]>=0 && arr[j]<=n)
				{
					freq[arr[j]]++;
				}
						
			}
			
			
			
			int num1 =0 , num2= 0 , k ;		
			for( k = 0 ; k <=n ; k++)
			{
				if(freq[k]==0)
				{
					num1 = k;
					freq[k]++;
					//System.out.println(k);
					break ;
				}
			}
			
			
			for(int s = 0 ; s<=num1 ; s++)
			{
				freq[s]--;
				if(freq[s]==0)
				{
					num2= s; 
					//System.out.println(s);
					break;
				}
			}
			System.out.println(num1+num2);
			
			
		}
		
		
		
		
		
		
			}
		
		
			
			
			
			
			
				
			
			
		
		
		
		
			
			
			
			
		}
	


