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.ArrayList;
import java.util.Collections;
import java.util.Deque;
import java.util.HashMap;
import java.util.LinkedList;


public class Unusual_Competitions {


  public static void main(String[] args) throws NumberFormatException, IOException {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    int t1=Integer.parseInt(br.readLine());
    for(int t=0;t<t1;++t)
    {
      int n=Integer.parseInt(br.readLine());
      ArrayList<Integer>al=new ArrayList<>();
      StringBuilder ans=new StringBuilder();
      for(int i=1;i<=2*n;++i)
      {
        al.add(i);
      }
      String s[]=br.readLine().trim().split(" ");

      for(String a:s)
      {
        Integer k=new Integer(a);
        al.remove(k);
      }
      boolean flag=true;
      for(String a:s)
      {
        Integer k=new Integer(a);
        ans.append(a+" ");
        int f=0;
        for(Integer i:al)
        {
          if(i>k)
          {
           f=1;
            ans.append(i+" ");
            al.remove(i);
            break;
          }

        }

        if(f==0)
        {
          System.out.println(-1);
          flag=false;
          break;
        }
      }
      if (flag) {
        System.out.println(ans);
      }




      }
    }
  }