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.*;

public class Main {

    public static void main(String[] args) {

        Scanner s = new Scanner(System.in);

        int t = s.nextInt();

        for(int p=0;p<t;p++){

            int n = s.nextInt();
            int[] arr = new int[n];

            for(int i=0;i<n;i++)
                arr[i]=s.nextInt();

            int[] prr = new int[2*n];
            int next = 0;
            boolean match=false,exceed=false;
            boolean sup=false;
            int k=0;

            l: for(int i=0;i<2*n-1;i=i+2){

               prr[i]=arr[k];

               next=arr[k]+1;

               while(true){
                   sup=false;

                   while(true){
                       match=false;

                       for(int j=0;j<n;j++){
                           if(next==arr[j]){
                               next++;
                               match=true;
                               sup=true;
                           }
                           if(next>2*n){
                               exceed=true;
                               break l;
                           }
                       }
                       if(!match)
                           break;
                   }

                   while(true){
                       match=false;

                       for(int j=0;j<2*n;j++){
                           if(next==prr[j]){
                               next++;
                               match=true;
                               sup=true;
                           }
                           if(next>2*n){
                               exceed=true;
                               break l;
                           }
                       }

                       if(!match)
                           break;
                   }

                   if(!sup)
                       break;
               }

                prr[i+1]=next;
                k++;
            }

            if(exceed)
                System.out.print("-1");
            else
                for(int i=0;i<2*n;i++)
                    System.out.print(prr[i] + " ");

            System.out.println();
        }
    }
}