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

/**
 * @author Finn Lidbetter
 */
import java.util.*;
import java.io.*;
import java.awt.geom.*;

public class TaskA {
  public static void main(String[] args) throws IOException {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringBuilder sb = new StringBuilder();
    
    int nTests = Integer.parseInt(br.readLine());
    for (int test=0; test<nTests; test++) {
      int n = Integer.parseInt(br.readLine());
      int[] arr = new int[n];
      String[] s = br.readLine().split(" ");
      for (int i=0; i<n; i++) {
        arr[i] = Integer.parseInt(s[i]);
      }
      Arrays.sort(arr);
      HashSet<Integer> a = new HashSet<>();
      HashSet<Integer> b = new HashSet<>();
      for (int i=0; i<n; i++) {
        if (a.contains(arr[i])) {
          b.add(arr[i]);
        } else {
          a.add(arr[i]);
        }
      }
      int mexA = 0;
      for (int i=0; i<200; i++) {
        if (!a.contains(i)) {
          mexA = i;
          break;
        }
      }
      int mexB = 0;
      for (int i=0; i<200; i++) {
        if (!b.contains(i)) {
          mexB = i;
          break;
        }
      }
      System.out.println(mexA + mexB);
    }
  }
  

}

class MyUtils {
  static void shuffleArray(int[] arr) {
    int n = arr.length;
    Random rnd = new Random();
    for(int i=0; i<n; i++) {
      int tmp = arr[i];
      int randomPos = i + rnd.nextInt(n-i);
      arr[i] = arr[randomPos];
      arr[randomPos] = tmp;
    }
  }
  static void shuffleArray(long[] arr) {
    int n = arr.length;
    Random rnd = new Random();
    for(int i=0; i<n; i++) {
      long tmp = arr[i];
      int randomPos = i + rnd.nextInt(n-i);
      arr[i] = arr[randomPos];
      arr[randomPos] = tmp;
    }
  }
}
