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 Asd {
     static Scanner s=new Scanner(System.in);
    static PrintWriter w=new PrintWriter(System.out);
 public static void main(String args[])
  {
        int t=s.nextInt();
    while(t-->0)
    {       
     solve();   
    }
    w.close();
   }
 public static void solve()
 {
     int n=s.nextInt();
     HashSet<Integer> set=new HashSet<>();
     ArrayList<Integer> list=new ArrayList<>();
     int arr[]=new int[n];
     
     for(int i=0;i<n;i++)
     {
         arr[i]=s.nextInt();
        
         set.add(arr[i]);
     }
     
     if(set.contains(2*n)||!set.contains(1))
     { w.println(-1);return;}
     
     for(int i=0;i<n;i++)
     {
         for(int j=1;true;j++)
         {
             if(!set.contains(arr[i]+j))
             {
                 if(arr[i]+j>2*n)
                 {
                     w.println(-1);return;
                 }
                 list.add(arr[i]);list.add(arr[i]+j);
                 
                 set.add(arr[i]+j);
                 break;
             }
             
         }
         
     }
     for(int i=0;i<list.size();i++)
         w.print(list.get(i)+" ");
     w.println();
     
 }
    
}