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.lang.reflect.Array;
import java.util.*;

// имя начинается с двух подчеркиваний, чтобы был первым в списке (он сортится по алфавиту)
public class A {

    // определяет, запускается решение "дома" или на CF/timus
    static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    public static void main(String[] args) {
        new A().run();
    }

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok;

    void init() throws FileNotFoundException {
        // иницилизация потоков вводилок/выводилок
        // System.in/System.out - стандартные потоки ввода/вывода на консоль

        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }

        tok = new StringTokenizer("");
    }

    void run() {
        try {
            long timeStart = System.currentTimeMillis();

            init();
            solve();

            out.close();

            long timeEnd = System.currentTimeMillis();
            System.err.println("Time = " + (timeEnd - timeStart));
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    // чтение строки вернет null, если ничего не осталось
    String readLine() throws IOException {
        return in.readLine();
    }

    // содержит символы, являющиеся "разделителями ввода"
    // по умолчанию это пробел (перевод строки автоматом учитывается)
    String delimiter = " ";

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            String nextLine = readLine();
            if (null == nextLine) return null;

            tok = new StringTokenizer(nextLine);
        }

        return tok.nextToken(delimiter);
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    // тут мы будем писать основное решение
    void solve() throws IOException {
        int t = readInt();
        while (t > 0) {
            findMex();
            t--;
        }
    }

    void findMex() throws IOException {
        int n = readInt();
        int sum = 0;
        ArrayList<Integer> que = new ArrayList<>();

        for (int i = 0; i < n; i++) {
            int tmpReaded = readInt();

            que.add(tmpReaded);
        }
        Collections.sort(que);

        int count = 0;
        if (que.get(count) != 0) {
            out.println(sum);
            return;
        }
        while (que.size() > 0) {
            if (count + 1 == que.size()) {
                sum += que.get(count) + 1;
                break;
            }
            if (que.get(count).equals( que.get(count + 1))) {
                count++;
                continue;
            }
            if (que.get(count + 1) - que.get(count) > 1) {
                sum += que.get(count) + 1;
                que.remove(count);
                break;
            }
            que.remove(count);
        }
        count = 0;
        if (que.get(count) != 0 || que.size() == 1) {
            out.println(sum);
            return;
        }
        while (que.size() > 0) {
            if (count + 1 == que.size()) {
                sum += que.get(count) + 1;
                break;
            }
            if (que.get(count).equals(que.get(count + 1))) {
                count++;
                continue;
            }
            if (que.get(count + 1) - que.get(count) > 1) {
                sum += que.get(count) + 1;
                que.remove(count);
                break;
            }
            que.remove(count);
        }
        out.println(sum);

    }

}