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:
/*
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 * and open the template in the editor.
 */

import java.io.*;
import java.util.*;
public class C1315 
{
    public static void main(String args[])throws IOException
        {
            Scanner sc=new Scanner(System.in);
            int t=sc.nextInt();
            for(int z=1;z<=t;z++)
            {
                int n=sc.nextInt();
                int b[]=new int[n];
                TreeSet<Integer> set=new TreeSet<>();
                for(int i=1;i<=2*n;i++)
                {
                    set.add(i);
                }
                for(int i=0;i<n;i++)
                {
                    b[i]=sc.nextInt();
                    set.remove(b[i]);
                }
                int a[]=new int[2*n];
                int f=0;
                for(int i=0;i<n;i++)
                {
                    a[2*i]=b[i];
                    if(set.higher(b[i])==null)
                    {
                        f=1;break;
                    }
                    int x=set.higher(b[i]);
                    a[2*i +1]=x;
                    set.remove(x);
                }
                if(f==1)
                    System.out.println(-1);
                else
                {
                    for(int i=0;i<2*n;i++)
                    {
                        System.out.print(a[i]+" ");
                    }
                    System.out.println();
                }
            }
        }

}