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:

import java.io.*;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;
 
 public class realfast implements Runnable {
    private static final int INF = (int) 1e9;
    long in= (long)Math.pow(10,9);
    public  void solve() throws IOException 
    {

     int t = readInt();
     for(int f =0;f<t;f++)
     {
       int n = readInt();
       int arr[]= new int [n];
       boolean check = true;
       boolean map[]= new boolean[2*n+1];
       for(int i =0;i<n;i++)
       {
         arr[i]= readInt();
         if(map[arr[i]])
         {
               check=false;          
         }
         map[arr[i]]=true;
       }
       int fin[]= new int[2*n];
       for(int i=0;i<n;i++)
       {
        fin[2*i]=arr[i];
       }
       for(int i=0;i<n;i++)
       {
         int val= arr[i];
         if(val==2*n)
         {
           check=false;
           break;
         }
         for(int j=val+1;j<=2*n;j++)
         {
              if(!map[j])
              {
                fin[2*i+1]= j;
                map[j]=true;
                break;
              }
              if(j==2*n)
              {
                check=false;
                break;
              }
         }
       }
       if(!check)
        out.println(-1);
       else
       {
          for(int i=0;i<2*n;i++)
            out.print(fin[i]+" ");
         out.println();
       }

     }
    }  
   
    ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
    public static void main(String[] args) {
        new Thread(null, new realfast(), "", 128 * (1L << 20)).start();
    }
 
    private static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    private BufferedReader reader;
    private StringTokenizer tokenizer;
    private PrintWriter out;
 
    @Override
    public void run() {
        try {
            if (ONLINE_JUDGE || !new File("input.txt").exists()) {
                reader = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                reader = new BufferedReader(new FileReader("input.txt"));
                out = new PrintWriter("output.txt");
            }
            solve();
        } catch (IOException e) {
            throw new RuntimeException(e);
        } finally {
            try {
                reader.close();
            } catch (IOException e) {
                // nothing
            }
            out.close();
        }
    }
 
    private String readString() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
 
    @SuppressWarnings("unused")
    private int readInt() throws IOException {
        return Integer.parseInt(readString());
    }
 
    @SuppressWarnings("unused")
    private long readLong() throws IOException {
        return Long.parseLong(readString());
    }
 
    @SuppressWarnings("unused")
    private double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }
}
class edge implements Comparable<edge>{
    int u ;
    int v ;
    int val;
    edge(int u1, int v1 , int val1)
    {
       this.u=u1;
       this.v=v1;
       this.val=val1;
    }
    public int compareTo(edge e)
    {
        return this.val-e.val;
    }
}