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.util.*;
import java.io.*;
 
  
   
     public class Solution{
         
         public static void main (String args[])throws IOException{
             
             BufferedReader ob = new BufferedReader(new InputStreamReader(System.in));
             
             
             int t = Integer.parseInt(ob.readLine());
             
             while(t --> 0){
                 int n = Integer.parseInt(ob.readLine());
                 
                 int []ar = new int[n];
                 int N = 2*n;
                 
                 LinkedList<Integer>queue = new LinkedList<>();
                 
                 StringTokenizer st = new StringTokenizer(ob.readLine());
                 TreeSet<Integer>set = new TreeSet<>();
                 
                 for(int i = 0; i < n; i++){
                     ar[i] = Integer.parseInt(st.nextToken());
                     set.add(ar[i]);
                 }
                 TreeSet<Integer>set1 = new TreeSet<>();
                 for(int i = 1; i <= N; i++){
                        if(!set.contains(i)){
                          set1.add(i);
                        }
                 }
                ArrayList<Integer>list = new ArrayList<>();
           
                for(int i = 0; i < n; i++){
                    list.add(ar[i]);
                       for(int a : set1){
                           if(a > ar[i]){
                               list.add(a);
                               set1.remove(a);
                               break;
                           }
                       }
                }
                     
                     
               if(list.size() < 2*n){
                   System.out.print(-1);
               }else{
                   for(int a : list){
                       System.out.print(a+" ");
                   }
               }
               System.out.println();
               }
             }
               }