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.*;
import java.util.*;
import java.lang.*;
import java.math.*;

public class Main
{
	public static void main(String[] args) throws IOException{
	    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	    int t=Integer.parseInt(br.readLine());
	    while (t-->0){
	        int n=Integer.parseInt(br.readLine());
	        Integer[] b=new Integer[2*n];
	        String s=br.readLine();
	        StringTokenizer st=new StringTokenizer(s);
	        for(int i=0;i<2*n;i+=2){
	          b[i]=Integer.parseInt(st.nextToken());
	          b[i+1]=b[i];
	        }
	        Set<Integer> set = new HashSet<Integer>(Arrays.asList(b));
	        Set<Integer> a=new TreeSet<Integer>();
	        for(int i=1;i<=2*n;i++){
	            if(!set.contains(i)){
	                a.add(i);
	            }
	        }
	        int flag=0;
	        for(int i=1;i<2*n;i+=2){
	            flag=0;
	            for(int it : a){
	                if(it>b[i]){
	                    b[i]=it;
	                    flag=1;
	                    a.remove(it);
	                    break;
	                }
	            }
	            if(flag==0){
	                System.out.println(-1);
	                break;
	            }
	        }
	        if(flag!=0){
	            for(int i=0;i<2*n;i++)
	              System.out.print(b[i]+" ");
	              System.out.println();
	        }
	    } 
	    
	}
}