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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Scanner;
public class CodeForce {
	public static void main(String[] args) throws IOException {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
                
                   int t=Integer.parseInt(br.readLine());
                   while(t-->0){
                      
                       int n=Integer.parseInt(br.readLine());
                int flag=0;
                HashSet<Integer> set1=new HashSet<>();
                HashSet<Integer> set2=new HashSet<>();
                        String[] s=br.readLine().split(" ");
                        int[] arr=new int[2*n];
                        for(int i=0;i<n;i++){
                            arr[i*2]=Integer.parseInt(s[i]);
                            set1.add(arr[i*2]);
                            if(arr[i*2]>=2*n){
                                flag=1;
                                break;
                            }
                        }
                        
                       if(flag==1){
                           System.out.println("-1");
                       }
                       else{
                           int te;
                           for(int i=1;i<2*n;i=i+2){
                               te=arr[i-1];
                               
                               while(true){
                                   if(!set1.contains(te) && !set2.contains(te))
                                   {
                                       break;
                                   }
                                   te++;
                               }
                               if(te>2*n)
                               { flag=1;
                                   break;
                               }
                               arr[i]=te;
                               set2.add(arr[i]);
                           }
                           if(flag==0){
                           for(int i=0;i<2*n;i++)
                               System.out.print(arr[i]+" ");
                           System.out.println(" ");
                           }
                           else
                               System.out.println(-1);
                       }
                                         }
                    
                    
                    
                }
		

}