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 a{
   static char[] count;
   // static int[] count1;
   static long[] arr;
   //static char[] c;
   static long[] darr;
   // static int x;
   static long maxl;
   // static long minl;
   static long mod = 998244353l;
   static int n;
   static long a;
   static long b;
   static long c;
   static long d;
   static int x;
   static long y;
   static int m;
   static long k;
   static String str;
   static Set<Long> set;
   // static Map<Long,Long> map;
   static StringBuilder sb;

   // public static int log(long n){
   //     if(n == 0)
   //         return 0;

   //     if(n == 1)
   //         return 0;
   //     if(n == 2)
   //         return 1;
   //     double num = Math.log(n);
   //     double den = Math.log(2);
   //     if(den == 0)
   //         return 0;
   //     return (int)(num/den);
   // }

   // public static void swap(int i,int j){
   //     long temp = arr[j];
   //     arr[j] = arr[i];
   //     arr[i] = temp;
   // }



   public static void solve(){

      SortedSet<Long> list1 = new TreeSet<>();
      SortedSet<Long> list2 = new TreeSet<>();
      Arrays.sort(arr);

      for(int i = 0 ; i < n; i++){
         if(list1.contains(arr[i]))
            list2.add(arr[i]);
         else
            list1.add(arr[i]);
      }

      long mex1 = 0;
      long mex2 = 0;
      for(Long i : list1){
         if(mex1 != i){
            break;
         }
         else
            mex1 += 1;
      }
      for(Long i : list2){
         if(mex2 != i){
            break;
         }
         else
            mex2 += 1;
      }

      System.out.println(mex1+mex2);

   }

   public static void main(String[] args) {

      Scanner sc = new Scanner(System.in);

      int t = sc.nextInt();
      while(t > 0){
         // set = new HashSet<>();
         // map = new HashMap<>();
//         a = sc.nextLong();
//         b = sc.nextLong();
//         c = sc.nextLong();
//         d = sc.nextLong();

         // long x = sc.nextLong();

         // maxl = Integer.MIN_VALUE;


         n = sc.nextInt();
         //k = sc.nextLong();
         // k = sc.nextInt();
         // // x = sc.nextInt();
         // // // c = sc.next().toCharArray();

         // // // k = sc.nextInt();
         arr = new long[n];
         // // // // // darr = new char[n];

          for(int i = 0; i < n ; i++){
              arr[i] = sc.nextLong();
          }



         // darr = new long[n];
         // for(int i = 0; i < n ; i++){
         //     darr[i] = sc.nextLong();
         // }
         // boolean flag = false;
         // str = sc.next();

         // x = sc.nextInt();



         //System.out.println(solve()?"Yes":"No");
         solve();
         //System.out.println(solve());
         // sb = new StringBuilder();
         // sb.append(str);

         t -= 1;
      }



   }
}