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 Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
	
	BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
	int t=Integer.parseInt(bf.readLine());
	while(t-->0)
	{
	    int n=Integer.parseInt(bf.readLine());
	    String s[]=bf.readLine().split(" ");
	    ArrayList<Integer> al=new ArrayList<>();
	    for(int i=0;i<n;i++)
	    {
	        al.add(Integer.parseInt(s[i]));
	    }
	    int range=2*n;
	    ArrayList<Integer> al2=new ArrayList<>();
	    boolean sangam=true;
	    for(int i=0;i<n;i++)
	    {
	        int z=al.get(i);
	        al2.add(z);
	        z++;
	        while(true)
	        {
	        if(al.contains(z) || al2.contains(z))
	        {
	            z++;
	            
	        }
	        else
	        {
	            
	            if(z<=range)
	            {
	                al2.add(z);
	                break;
	            }
	            else
	            {
	                sangam=false;
	                break;
	            }
	        }
	        }
	        if(sangam==false)
	        {
	            break;
	        }
	    }
//	    System.out.println(al);
//	    System.out.println(al2);
	    if(sangam)
	    {
	        for(int i=0;i<al2.size();i++)
	        {
	            System.out.print(al2.get(i)+" ");
	        }
	        System.out.println();
	    }
	    else
	    {
	        System.out.println(-1);
	    }
	    
	}
	
	}
}