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.ArrayList;
import java.util.List;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class Mex {

    private static long mex(List<Long> set) {

        if (set.size() == 0)
            return 0;

        sort(set);
        long val = 0;

        long mexA = -1;
        long mexB = -1;

        boolean isA = true;
        boolean bOver = false;

        for (int i = 0; i < set.size(); i += 1) {
            long curr = set.get(i);

            if (curr == val && mexA == curr && mexA == mexB)
                continue;


            if (curr == val + 1) {
                if (mexA == -1)
                    break;
                val = curr;
                if (!isA) {
                    bOver = true;
                    isA = true;
                }
            } else if (curr > val + 1) {
                break;
            }

            if (isA) {
                mexA = curr;
                if (!bOver)
                    isA = false;
            } else {
                mexB = curr;
                isA = true;
            }
        }

        return mexA + mexB + 2;

    }

    public static void sort(List A) {
        PriorityQueue pq = new PriorityQueue();
        int i = 0;
        for (i = 0; i < A.size(); i++)
            pq.add(A.get(i));

        for (i = 0; i < A.size(); i++)
            A.set(i, pq.poll());
    }

    public static void main(String[] args) {

        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));

        int nb = sc.nextInt();
        for (int i = 0; i < nb; i++) {
            int nb2 = sc.nextInt();
            List<Long> set = new ArrayList<>();
            for (int j = 0; j < nb2; j++) {
                set.add(sc.nextLong());
            }
            out.println(mex(set));
        }
        out.close();

    }

    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }

}
