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:
/* package codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
   
    public static void resPermu(int[] arr, int n){
        
        HashSet<Integer> hset = new HashSet<Integer>();
        
        for(int i = 0 ;i<n ;i++)
           hset.add(arr[i]);
       
        int max= 0;
        int[] result = new int[2*n];
        int index =0;
        for(int i = 0 ;i<n;i++){
           result[index] = arr[i];
           int curr = arr[i];
           while(hset.contains(curr)){
               curr++;
               
           }
           index++;
           if(curr>max)
             max = curr;
           result[index] = curr;
           index++;
           hset.add(curr);
                  
        }
        
        if(max>(n*2)){
            System.out.print(-1);
        }else{
            for(int i = 0;i<2*n;i++){
                System.out.print(result[i]+" ");
                
            }
            
        }
        
        System.out.println();
        return;
        
    }
    
	public static void main (String[] args) throws java.lang.Exception
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int itr = Integer.parseInt(br.readLine());
		while(itr-->0){
		    
		          int n  =  Integer.parseInt(br.readLine());
		          String[] s   =br.readLine().split(" ");
		          int[] arr = new int[n];
		          for(int i = 0 ;i<n ;i++)
		            arr[i] = Integer.parseInt(s[i]);
		            
		           resPermu(arr,n);
		    
		    
		}
	}
}