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.util.*;import java.io.*;import java.math.*;
	public class D
	{
	    static final Random random=new Random();
	    static boolean memory = true;
	    
	    static void ruffleSort(int[] a) {
	        int n = a.length; 
	        for (int i=0; i<n; i++) {
	            int oi=random.nextInt(n), temp=a[oi];
	            a[oi]=a[i]; a[i]=temp;
	        }
	        ArrayList<Integer> lst = new ArrayList<>();
	        for(int i : a)
	            lst.add(i);
	        Collections.sort(lst);
	        for(int i = 0; i < n; i++)
	            a[i] = lst.get(i);
	    }
	
	    static void ruffleSort(long[] a) {
	        int n = a.length; 
	        for (int i=0; i<n; i++) {
	            int oi=random.nextInt(n);
	            long temp=a[oi];
	            a[oi]=a[i]; a[i]=temp;
	        }
	        ArrayList<Long> lst = new ArrayList<>();
	        for(long i : a)
	            lst.add(i);
	        Collections.sort(lst);
	        for(int i = 0; i < n; i++)
	            a[i] = lst.get(i);
	    }
	    static Set<String> se = new HashSet<>();
		public static void process(int[] a1)throws IOException
		{	
			int n=ii();
			int[] ar = iai(n);
//			Arrays.sort(ar);
			int ans=0;
			List<Integer> a=  new ArrayList<>();
			for(int i=0;i<n;i++) {
				List<Integer> b=  new ArrayList<>();
				a.add(ar[i]);
				for(int j=i+1;j<n;j++) {
					b.add(ar[j]);
				}
				int mina=0,minb=0;
				for(int j=0;j<=101;j++) {
					if(!a.contains(j)) {
						mina=j;
						break;
					}
				}
				for(int j=0;j<=101;j++) {
					if(!b.contains(j)) {
						minb=j;
						break;
					}
				}
//				System.out.println(mina+" "+minb);
				ans=Math.max(ans, mina+minb);
			}
			System.out.println(ans);
		}
	    static AnotherReader sc;
	    static PrintWriter out;
	
	    public static void main(String[] args) throws Exception{
	        if(memory)new Thread(null, new Runnable() {public void run(){try{new D().run();}catch(Exception e){e.printStackTrace();System.exit(1);}}}, "1", 1 << 28).start();
	        else new D().run();
	    }
	    void run()throws Exception
	    {
	        boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	        if(oj){sc=new AnotherReader();out=new PrintWriter(System.out);}
	        else{sc=new AnotherReader(100);out=new PrintWriter("output.txt");}
	        long s = System.currentTimeMillis();
	        long max = 1000000+3;
	        int[] cnt = new int[(int) max];
//	        Arrays.fill(cnt, 1);
//	        for(int i=2;i<=1000;i++) {
//	        	for(int j=2*i;j<=max;j+=i) {
//	        		cnt[j]=0;
//	        	}
//	        }
	        
	        int t=1;
	        t=ii();
	        //int k = t;
	        while(t-->0) {/*p("Case #"+ (k-t) + ": ")*/;process(cnt);}
	        out.flush();
	        System.err.println(System.currentTimeMillis()-s+"ms");
	        out.close();
	    }
	
	    static long power(long k, long c, long mod){
	        long y = 1;
	        while(c > 0){
	            if(c%2 == 1)
	                y = y * k % mod;
	            c = c/2;
	            k = k * k % mod;
	        }
	        return y;
	    }
	
	    static int power(int x, int y, int p){ 
	        int res = 1;
	        x = x % p;
	        while (y > 0) {
	            if (y % 2 == 1)
	                res = (res * x) % p;
	            y = y >> 1;
	            x = (x * x) % p;
	        }
	        return res;
	    }
	
	    static int log2(int N)
	    {
	        int result = (int)(Math.log(N) / Math.log(2));
	        return result;
	    }
	
	 
	    static void pn(Object o){out.println(o);}
	    static void p(Object o){out.print(o);}
	    static void pni(Object o){out.println(o);out.flush();}
	    static int ii()throws IOException{return sc.nextInt();}
	    static long ll()throws IOException{return sc.nextLong();}
	    static double nd()throws IOException{return sc.nextDouble();}
	    static String iln()throws IOException{return sc.nextLine();}
	    static int[] iai(int N)throws IOException{int[]A=new int[N];for(int i=0;i!=N;i++){A[i]=ii();}return A;}
	    static long[] ial(int N)throws IOException{long[]A=new long[N];for(int i=0;i!=N;i++){A[i]=ll();}return A;}
	    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
	    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
	    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}
	    
	/////////////////////////////////////////////////////////////////////////////////////////////////////////
	 
	    static class AnotherReader{BufferedReader br; StringTokenizer st;
	    AnotherReader()throws FileNotFoundException{
	    br=new BufferedReader(new InputStreamReader(System.in));}
	    AnotherReader(int a)throws FileNotFoundException{
	    br = new BufferedReader(new FileReader("C:\\Users\\Utkarsh\\OneDrive\\Desktop\\input1.txt"));}
	    String next()throws IOException{
	    while (st == null || !st.hasMoreElements()) {try{
	    st = new StringTokenizer(br.readLine());}
	    catch (IOException  e){ e.printStackTrace(); }}
	    return st.nextToken(); } int nextInt() throws IOException{
	    return Integer.parseInt(next());}
	    long nextLong() throws IOException
	    {return Long.parseLong(next());}
	    double nextDouble()throws IOException { return Double.parseDouble(next()); }
	    String nextLine() throws IOException{ String str = ""; try{
	    str = br.readLine();} catch (IOException e){
	    e.printStackTrace();} return str;}}
	
	/////////////////////////////////////////////////////////////////////////////////////////////////////////////
	}