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

/*****Author: Satyajeet Singh************************************/
    import java.io.*;
    import java.util.*;
    import java.text.*; 
    import java.lang.*;
    import java.math.*;
public class Main{
/*********************************************Constants******************************************/
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));        
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static long mod=(long)1e9+7;
    static long mod1=998244353;
    static ArrayList<Integer> graph[];
    static int pptr=0,pptrmax=0;
    static String st[];
/*****************************************Solution Begins***************************************/        

    public static void main(String args[]) throws Exception{
        int tt=pi();
        while(tt-->0){
            int n=pi();
            int input[]=new int[102];
            for(int i=0;i<n;i++)input[pi()]++;
            boolean flag=false;
            int ans=0;
            for(int i=0;i<=101;i++){
                if(input[i]>=2)continue;
                if(flag){
                    if(input[i]==1)continue;
                    else{
                        ans+=i;
                        break;
                    }
                }
                else{
                    if(input[i]==0){
                        ans+=2*i;
                        break;
                    }
                    else{
                        flag=true;
                        ans+=i;
                    }
                }
            }
            out.println(ans);
           
        }
/****************************************Solution Ends**************************************************/
        clr();
    }
    static void clr(){
        out.flush();
        out.close();
    }
    static void nl() throws Exception{
        pptr=0;
        st=br.readLine().split(" ");
        pptrmax=st.length;
    }
    static void nls() throws Exception{
        pptr=0;
        st=br.readLine().split("");
        pptrmax=st.length;
    }
    static int pi() throws Exception{
        if(pptr==pptrmax)
            nl();
        return Integer.parseInt(st[pptr++]);
    }
    static long pl() throws Exception{
        if(pptr==pptrmax)
            nl();
        return Long.parseLong(st[pptr++]);
    }
    static double pd() throws Exception{
        if(pptr==pptrmax)
            nl();
        return Double.parseDouble(st[pptr++]);
    }
    static String ps() throws Exception{
        if(pptr==pptrmax)
            nl();
        return st[pptr++];
    }
/***************************************Precision Printing**********************************************/
    static void printPrecision(double d){
        DecimalFormat ft = new DecimalFormat("0.00000000000"); 
        out.println(ft.format(d));
    }
/**************************************Bit Manipulation**************************************************/
    static int countBit(long mask){
        int ans=0;
        while(mask!=0){
            mask&=(mask-1);
            ans++;
        }
        return ans;
    }
/******************************************Graph*********************************************************/
    static void Makegraph(int n){
        graph=new ArrayList[n];
        for(int i=0;i<n;i++)
            graph[i]=new ArrayList<>();
    }
    static void addEdge(int a,int b){
        graph[a].add(b);
    }
    // static void addEdge(int a,int b,int c){
    //     graph[a].add(new Pair(b,c));
    // }    
/*********************************************PAIR********************************************************/
    static class Pair{
        int u;
        int v;
        public Pair(int u, int v) {
            this.u = u;
            this.v = v;
        }
        public int hashCode() {
            int hu = (int) (u ^ (u >>> 32));
            int hv = (int) (v ^ (v >>> 32));
            return 31 * hu + hv;
        }
        public boolean equals(Object o) {
            Pair other = (Pair) o;
            return u == other.u && v == other.v;
        }
        public String toString() {
            return "[u=" + u + ", v=" + v + "]";
        }
    }
/******************************************Long Pair*******************************************************/
    static class Pairl{
        long u;
        long v;
        public Pairl(long u, long v) {
            this.u = u;
            this.v = v;
        }
        public int hashCode() {
            int hu = (int) (u ^ (u >>> 32));
            int hv = (int) (v ^ (v >>> 32));
            return 31 * hu + hv;
        }
        public boolean equals(Object o) {
            Pairl other = (Pairl) o;
            return u == other.u && v == other.v;
        }
        public String toString() {
            return "[u=" + u + ", v=" + v + "]";
        }
    }
/*****************************************DEBUG***********************************************************/
    public static void debug(Object... o){
        System.out.println(Arrays.deepToString(o));
    }
/************************************MODULAR EXPONENTIATION***********************************************/
    static long modulo(long a,long b,long c){
        long x=1,y=a%c;
        while(b > 0){
            if(b%2 == 1)
                x=(x*y)%c;
            y = (y*y)%c;
            b = b>>1;
        }
        return  x%c;
    }
/********************************************GCD**********************************************************/
    static long gcd(long x, long y){
        if(x==0)
            return y;
        if(y==0)
            return x;
        long r=0, a, b;
        a = (x > y) ? x : y; 
        b = (x < y) ? x : y;
        r = b;
        while(a % b != 0){
            r = a % b;
            a = b;
            b = r;
        }
        return r;
    }
}