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.DataInputStream;
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import static java.lang.System.out;
import java.util.*;
import java.util.Map.Entry;
import javax.crypto.AEADBadTagException;



public class Main 
{
    public static void main(String[] args) throws Exception
    {
        
        long start = System.currentTimeMillis();
        
        /*
        FileWriter writer = new FileWriter("input.txt");
        
        for(int i=0;i<1000;++i)
        {
            int val = Mother_Class.getRandomInteger(1, 100000);
            writer.write(val+"\n");
            for(int j=0;j<val;++j)
            {
                writer.write(j+" ");
            }
            writer.write("\n");
        }
        
        writer.close();
        */
        
        
        Reader read = new Reader();
        
        int test, n;
        test = read.inte();
        
        while(test-- > 0)
        {
            n = read.inte();
            int[] count = new int[101];
            for(int i=0;i<n;++i) { int x = read.inte(); ++count[x]; }
            
            int[] A = new int[101];
            int[] B = new int[101];
            
            for(int i=0;i<101;++i)
            {
                if(count[i]>0)
                {
                    ++A[i];
                    --count[i];
                }
                if(count[i]>0)
                {
                    ++B[i];
                    --count[i];
                }
            }
            
            int sum = 0;
            
            for(int i=0;i<101;++i)
            {
                if(A[i]==0) { sum += i; break; }
            }
            for(int i=0;i<101;++i)
            {
                if(B[i]==0) { sum += i; break; }
            }
            out.println(sum);
        }
        
        long end = System.currentTimeMillis();
        
        //out.println("Execution Time: "+(end-start)+"ms");
        
    }
    
    
}

class Pair
{
    public int first;
    public int second;

    public Pair(int first, int second)
    {
        this.first = first;
        this.second = second;
    }

    @Override
    public String toString()
    {
        return "{"+first+", "+second+"}";
    }

    
}

class CustomCompare implements Comparator<Pair>
{

    @Override
    public int compare(Pair o1, Pair o2) 
    {
        return o1.first - o2.first;
    }
    
}

class Triplet
{
    public int first;
    public int second;
    public int third;

    public Triplet(int first, int second, int third)
    {
        this.first = first;
        this.second = second;
        this.third = third;
    }

    @Override
    public String toString()
    {
        return "{"+first+", "+second+", "+third+"}";
    }
}



class Reader 
{
    final private int BUFFER_SIZE = 1 << 16;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;

    public Reader()
    {
        din = new DataInputStream(System.in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public Reader(String file_name) throws IOException
    {
        din = new DataInputStream(
            new FileInputStream(file_name));
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public String stren() throws IOException
    {
        byte[] buf = new byte[500000]; // line length
        int cnt = 0, c;
        while ((c = read()) != -1) {
            if (c == '\n') {
                if (cnt != 0) {
                    break;
                }
                else {
                    continue;
                }
            }
            buf[cnt++] = (byte)c;
        }
        return new String(buf, 0, cnt);
    }

    public String strsp() throws IOException
    {
        byte[] buf = new byte[500000]; // line length
        int cnt = 0, c;
        while ((c = read()) != -1) {
            if (c == ' ' || c == '\n') {
                if (cnt != 0) {
                    break;
                }
                else {
                    continue;
                }
            }
            buf[cnt++] = (byte)c;
        }
        return new String(buf, 0, cnt);
    }

    public int inte() throws IOException
    {
        int ret = 0;
        byte c = read();
        boolean eof = false;
        while (c <= 47 || c >= 58) 
        {
            if(c==45) { break; }
            if(c==-1) { eof = true; break; }
            c = read();
        }
        if(eof) { return Integer.MIN_VALUE; }
        
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');

        if (neg)
            return -ret;
        return ret;
    }

    public long lon() throws IOException
    {
        long ret = 0;
        byte c = read();
        boolean eof = false;
        while (c <= 47 || c >= 58) 
        {
            if(c==45) { break; }
            if(c==-1) { eof = true; break; }
            c = read();
        }
        if(eof) { return Long.MIN_VALUE; }
        
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (neg)
            return -ret;
        return ret;
    }

    public double dbl() throws IOException
    {
        double ret = 0, div = 1;
        byte c = read();
        boolean eof = false;
        while (c <= 47 || c >= 58) 
        {
            if(c==45) { break; }
            if(c==-1) { eof = true; break; }
            c = read();
        }
        if(eof) { return Double.NEGATIVE_INFINITY; }
        
        boolean neg = (c == '-');
        if (neg)
            c = read();

        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');

        if (c == '.') {
            while ((c = read()) >= '0' && c <= '9') {
                ret += (c - '0') / (div *= 10);
            }
        }

        if (neg)
            return -ret;
        return ret;
    }

    private void fillBuffer() throws IOException
    {
        bytesRead = din.read(buffer, bufferPointer = 0,
                             BUFFER_SIZE);
        if (bytesRead == -1)
            buffer[0] = -1;
    }

    private byte read() throws IOException
    {
        if (bufferPointer == bytesRead)
            fillBuffer();
        return buffer[bufferPointer++];
    }

    public void close() throws IOException
    {
        if (din == null)
            return;
        din.close();
    }
}