Problem: You are given a sequence b_1, b_2, …, b_n. Find the lexicographically minimal permutation a_1, a_2, …, a_{2n} such that b_i = min(a_{2i-1}, a_{2i}), or determine that it is impossible.

Input

Each test contains one or more test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100).

The first line of each test case consists of one integer n — the number of elements in the sequence b (1 ≤ n ≤ 100).

The second line of each test case consists of n different integers b_1, …, b_n — elements of the sequence b (1 ≤ b_i ≤ 2n).

It is guaranteed that the sum of n by all test cases doesn't exceed 100.

Output

For each test case, if there is no appropriate permutation, print one number -1.

Otherwise, print 2n integers a_1, …, a_{2n} — required lexicographically minimal permutation of numbers from 1 to 2n.

Example

Input


5
1
1
2
4 1
3
4 1 3
4
2 3 4 5
5
1 5 7 2 8


Output


1 2 
-1
4 5 1 2 3 6 
-1
1 3 5 6 7 9 2 4 8 10 

Solution (in JAVA):

Solution:
/**
 * ******* Created  on 23/2/20 10:07 PM*******
 */

import java.io.*;
import java.util.*;

public class C1315 implements Runnable {

    private static final int MAX = (int) (1E5 + 5);
    private static final int MOD = (int) (1E9 + 7);
    private static final long Inf = (long) (1E14 + 10);

    private void solve() throws IOException {
        int t = reader.nextInt();
        int[] b = new int[105];
        int[] a = new int[210];
        List<Integer>list = new ArrayList<>();
        Set<Integer>set = new HashSet<>();
        while(t-->0){
            set.clear();
            int n = reader.nextInt();
            for(int i=1;i<=n;i++) {
                b[i] = reader.nextInt();
                set.add(b[i]);
            }
            boolean flag = true;
            for(int i=1;i<=n; i++){
                int val = 2*n+1;
                for(int j=b[i]+1;j<=2*n;j++){
                       if(!set.contains(j)){
                           val =j;break;
                       }
                }
                if(val > 2*n)
                    flag =false;
                a[2*i-1]=b[i];
                a[2*i]= val;
                set.add(val);
            }
            set.clear();
            for(int i=1;i<=2*n;i++){
                if(set.contains(a[i]))
                    flag =false;
                set.add(a[i]);
            }
            if(!flag)
                writer.print("-1");
            else
                for(int i=1;i<=2*n;i++)
                    writer.print(a[i]+" ");
            writer.println();
        }
    }

    public static void main(String[] args) throws IOException {
        try (Input reader = new StandardInput(); PrintWriter writer = new PrintWriter(System.out)) {
            new C1315().run();
        }
    }

    StandardInput reader;
    PrintWriter writer;

    @Override
    public void run() {
        try {
            reader = new StandardInput();
            writer = new PrintWriter(System.out);
            solve();
            reader.close();
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    interface Input extends Closeable {
        String next() throws IOException;

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

        default long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        default double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        default int[] readIntArray() throws IOException {
            return readIntArray(nextInt());
        }

        default int[] readIntArray(int size) throws IOException {
            int[] array = new int[size];
            for (int i = 0; i < array.length; i++) {
                array[i] = nextInt();
            }
            return array;
        }

        default long[] readLongArray(int size) throws IOException {
            long[] array = new long[size];
            for (int i = 0; i < array.length; i++) {
                array[i] = nextLong();
            }
            return array;
        }
    }

    private static class StandardInput implements Input {
        private final BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));

        private StringTokenizer stringTokenizer;

        @Override
        public void close() throws IOException {
            reader.close();
        }

        @Override
        public String next() throws IOException {
            if (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
                stringTokenizer = new StringTokenizer(reader.readLine());
            }
            return stringTokenizer.nextToken();
        }
    }
}