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.BufferedReader;
import java.util.Scanner;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Iterator;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.math.BigInteger;
public class A670
{
	static Scanner sc = new Scanner(System.in);
	static PrintWriter out = new PrintWriter(System.out);

	static void pn(Object o) {
		out.println(o);
		out.flush();

	}

	static void p(Object o) {
		out.print(o);
		out.flush();
	}

	static void pni(Object o) {
		out.println(o);
		System.out.flush();
	}

	static int I() throws IOException {
		return sc.nextInt();
	}

	static long L() throws IOException {
		return sc.nextLong();
	}

	static double D() throws IOException {
		return sc.nextDouble();
	}

	static String S() throws IOException {
		return sc.next();
	}

	static char C() throws IOException
	{
		return sc.next().charAt(0);
	}
static int[] Ai(int n) throws IOException
{
	int[] arr = new int[n];

	for (int i = 0; i < n; i++)
		arr[i] = I();

	return arr;
}

static String[] As(int n) throws IOException
{
	String s[] = new String[n];

	for (int i = 0; i < n; i++)
		s[i] = S();

	return s;
}

static long[] Al(int n) throws IOException 
{
	long[] arr = new long[n];

	for (int i = 0; i < n; i++)
		arr[i] = L();

	return arr;
}
public 	static void process() throws IOException
{
	int n=I();
	int[] arr=Ai(n);
	int cnt[]= new int[101];
	for(int s:arr)
	{
		cnt[s]++;
    }
	int c=0;int d=0;
	for(int i=0;i<101;i++)
	{
		if(cnt[i]==0)
		{
			c=i;
			break;
		}
	}
	for(int i=0;i<101;i++)
	{
		if(cnt[i]==1)
		{
			d=i;
			break;
		}
	}
	if(c<d)
	{
		pn(c+c);
	}
	else
	{
		pn(c+d);
	}
}

public static void main(String[] args) throws IOException {
	int t = I();
	while (t-- > 0)

		process();
}

	}