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.*;
import java.util.*;

public class SubsetMex {
    private static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private static final PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    private static final long[] POWERS_OF_TEN = { 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000,
            1000000000, 10000000000L, 100000000000L, 1000000000000L, 10000000000000L, 100000000000000L,
            1000000000000000L, 10000000000000000L, 100000000000000000L, 1000000000000000000L };
    private static StringTokenizer st;

    public static int gcd(int a, int b) {
        int res = 0;
        if (b > a) {
            int temp = a;
            a = b;
            b = temp;
        }
        while (b > 0) {
            int temp = b;
            b = a % b;
            a = temp;
            res = a;
        }
        return res;
    }

    private static int readInt() throws IOException {
        while (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return Integer.parseInt(st.nextToken());
    }

    private static Long readLong() throws IOException {
        while (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return Long.parseLong(st.nextToken());
    }

    private static String readToken() throws IOException {
        while (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    public static void main(String[] args) throws IOException {
        int T = readInt();
        while (T-- > 0)
            solve();
        pw.close();
    }

    private static void solve() throws IOException {
        int len = readInt();
        int[] ans = new int[101];
        int maxv2 = -1;
        int maxv1 = -1;
        boolean dothething = true;
        for (int i = 0; i < len; i++) {
            int temp = readInt();
            ans[temp]++;
        }
        for (int i = 0; i < 101; i++) {
            if (ans[i] > 1) {
                if (dothething)
                    maxv2 = i;
                maxv1 = i;
            } else if (ans[i] > 0) {
                maxv1 = i;
                dothething = false;
            } else {
                break;
            }
        }
        //if (maxv2 != -1) {
            maxv2++;
        //}
        //if (maxv1 != -1) {
            maxv1++;
        //}
        pw.println(maxv2 + maxv1);
    }
}
