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.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;
public class Main{
    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] nextArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }
        long[] nextArray(long n) {
            long[] a = new long[(int) n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }
    static class FastWriter extends PrintWriter {
        FastWriter(){
            super(System.out);
        }
        void println(int[] array) {
            for(int i=0; i<array.length; i++) {
                print(array[i]+" ");
            }
            println();
        }
        void println(long [] array) {
            for(int i=0; i<array.length; i++) {
                print(array[i]+" ");
            }
            println();
        }
    }
    static int MOD=998244353;
    public static void main(String[] args){
        FastScanner in = new FastScanner();
        FastWriter out = new FastWriter();
        int t=in.nextInt();
        //int t=1;
        while (t-->0){
            int n=in.nextInt();
            int[] ar=in.nextArray(n);
            HashMap<Integer,Integer> map=new HashMap<>();
            for (int i = 0; i < n; i++) {
                map.put(ar[i],map.getOrDefault(ar[i],0)+1);
            }
            int ans=0;boolean flag1=false;
            for (int i = 0; i < 102; i++) {
                int cnt=map.getOrDefault(i,0);
                if(cnt==0){
                    if(flag1){
                        ans+=i;
                    }else {
                        ans+=2*i;
                    }
                    break;
                }else if(cnt==1&&!flag1){
                    ans+=i;
                    flag1=true;
                }
            }
            out.println(ans);
        }
        out.close();
    }
    //Arrays.sort(a, (o1, o2) -> (o1[0] - o2[0]));
    static int subarray_lessthan_k(int[] A,int n,int k){
        int s=0,e=0,sum=0,cnt=0;
        while(e<n){
            sum+=A[e];
            while(s<=e&&sum>k){
                sum-=A[s++];
            }
            cnt+=e-s+1;
            e++;
        }
        return cnt;
    }
    static int diff(int num1,int num2) {
        String s1 = String.valueOf(num1);
        String s2 = String.valueOf(num2);
        if (s1.length() < s2.length()) {
            s1 = "0" + s1;
        }else if(s1.length()>s2.length()){
            s2="0"+s2;
        }
        int cnt=0;
        for (int i = 0; i < s1.length(); i++) {
            if(s1.charAt(i)!=s2.charAt(i)){
                cnt++;
            }
        }
        return cnt;
    }
    static int totalPrimeFactors(int n) {
        int cnt=0;
        while (n%2==0) {
            cnt++;
            n /= 2;
        }
        int num= (int) Math.sqrt(n);
        for (int i = 3; i <= num; i+= 2) {
            while (n%i == 0) {
                cnt++;
                n /= i;
                num=(int)Math.sqrt(n);
            }
        }
        if (n > 2){
            cnt++;
        }
        return cnt;
    }
    static char get(int i){
        return (char)(i+'a');
    }
    static boolean distinct(int num){
        HashSet<Integer> set=new HashSet<>();
        int len=String.valueOf(num).length();
        while (num!=0){
            set.add(num%10);
            num/=10;
        }
        return set.size()==len;
    }
    static int maxSubArraySum(int a[],int st,int en) {
        int max_s = Integer.MIN_VALUE, max_e = 0,ind=0,ind1=1;
        for (int i = st; i <= en; i++) {
            max_e+= a[i];
            if (max_s < max_e){
                max_s = max_e;
                ind=ind1;
            }
            if (max_e < 0){
                max_e = 0;
                ind1=i+1;
            }
        }
        if(st==0){
            return max_s;
        }
        if(ind==1){
            return a[0]+2*max_s;
        }else {
            return 2*max_s+maxSubArraySum(a,0,ind-1);
        }
        //return max_s;
    }
    static void segmentedSieve(ArrayList<Integer> res,int low, int high) {
        if(low < 2){
            low = 2;
        }
        ArrayList<Integer> prime = new ArrayList<>();
        simpleSieve(high, prime);
        boolean[] mark = new boolean[high - low + 1];
        for (int i = 0; i < mark.length; i++){
            mark[i] = true;
        }
        for (int i = 0; i < prime.size(); i++) {
            int loLim = (low / prime.get(i)) * prime.get(i);
            if (loLim < low){
                loLim += prime.get(i);
            }
            if (loLim == prime.get(i)){
                loLim += prime.get(i);
            }
            for (int j = loLim; j <= high; j += prime.get(i)) {
                mark[j - low] = false;
            }
        }
        for (int i = low; i <= high; i++) {
            if (mark[i - low]){
                res.add(i);
            }
        }
    }
    static void simpleSieve(int limit, ArrayList<Integer> prime) {
        int bound = (int)Math.sqrt(limit);
        boolean[] mark = new boolean[bound + 1];
        for (int i = 0; i <= bound; i++){
            mark[i] = true;
        }
        for (int i = 2; i * i <= bound; i++) {
            if (mark[i]) {
                for (int j = i * i; j <= bound; j += i){
                    mark[j] = false;
                }
            }
        }
        for (int i = 2; i <= bound; i++) {
            if (mark[i]){
                prime.add(i);
            }
        }
    }
    static int highestPowerOf2(int n) {
        if (n < 1){ return 0; }
        int res = 1;
        for (int i = 0; i < 8 * Integer.BYTES; i++) {
            int curr = 1 << i;
            if (curr > n){ break; }
            res = curr;
        }
        return res;
    }
    static int reduceFraction(int x, int y) {
        int d= gcd(x, y);
        return x/d+y/d;
    }
    static boolean subset(int[] ar,int n,int sum){
        if(sum==0){
            return true;
        }
        if(n<0||sum<0){
            return false;
        }
        return subset(ar,n-1,sum)||subset(ar,n-1,sum-ar[n]);
    }
    static boolean isPrime(int n){
        if(n<=1) return false;
        for(int i = 2;i<=Math.sqrt(n);i++){
            if (n % i == 0) return false;
        }
        return true;
    }
    static int gcd(int a, int b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }
    static long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }
    static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }
    static int lcm(int a, int b) {
        return (a * b) / gcd(a, b);
    }
    static boolean isPowerOfTwo(long n) {
        if(n==0){
            return false;
        }
        while (n%2==0){
            n/=2;
        }
        return n==1;
    }
    static boolean isPerfectSquare(int x){
        if (x >= 0) {
            int sr = (int)Math.sqrt(x);
            return ((sr * sr) == x);
        }
        return false;
    }
    static int lower_bound(int[] arr, int x) {
        int low_limit = 0, high_limit = arr.length, mid;
        while (low_limit < high_limit) {
            mid = (low_limit + high_limit) / 2;
            if (arr[mid] >= x){
                high_limit = mid;
            }else{
                low_limit = mid + 1;
            }
        }
        return low_limit;
    }
    static int upper_bound(int[] arr, int x) {
        int low_limit = 0, high_limit = arr.length, mid;
        while (low_limit < high_limit) {
            mid = (low_limit + high_limit) / 2;
            if (arr[mid] > x){
                high_limit = mid;
            }else{
                low_limit = mid + 1;
            }
        }
        return low_limit;
    }
    static int binarySearch(int[] ar,int n,int num){
        int low=0,high=n-1;
        while (low<=high){
            int mid=(low+high)/2;
            if(ar[mid]==num){
                return mid;
            }else if(ar[mid]>num){
                high=mid-1;
            }else {
                low=mid+1;
            }
        }
        return -1;
    }
    static int fib(int n) {
        long F[][] = new long[][]{{1,1},{1,0}};
        if (n == 0){
            return 0;
        }
        power(F, n-1);
        return (int)F[0][0];
    }
    static void multiply(long F[][], long M[][]) {
        long x =  (F[0][0]*M[0][0])%1000000007 + (F[0][1]*M[1][0])%1000000007;
        long y =  (F[0][0]*M[0][1])%1000000007 + (F[0][1]*M[1][1])%1000000007;
        long z =  (F[1][0]*M[0][0])%1000000007 + (F[1][1]*M[1][0])%1000000007;
        long w =  (F[1][0]*M[0][1])%1000000007 + (F[1][1]*M[1][1])%1000000007;
        F[0][0] = x%1000000007;
        F[0][1] = y%1000000007;
        F[1][0] = z%1000000007;
        F[1][1] = w%1000000007;
    }
    static void power(long F[][], int n) {
        if( n == 0 || n == 1){
            return;
        }
        long M[][] = new long[][]{{1,1},{1,0}};
        power(F, n/2);
        multiply(F, F);
        if (n%2 != 0){
            multiply(F, M);
        }
    }
}