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 Restoring_Permutation
{
	public static void main(String args[])
	{
		Scanner sc = new Scanner(System.in);
		int a = sc.nextInt();
		for(int i=0;i<a;i++)
		{
			int n=sc.nextInt();
			int data[] = new int[n];
			
			int man[] = new int[2*n];
			for(int j=0;j<n;j++)
				{
					data[j] = sc.nextInt();
					man[data[j]-1]=1;
				}
			
			
			//System.out.println(man[2*n-1]);
			if(man[2*n-1]==1)
				System.out.println(-1);
			else
			{
				int c[] = new int[n];
				for(int d=0;d<n;d++)
				c[d]=data[d];
		        
				Arrays.sort(c);
				int cnt=0;
				

    				for(int j=c[0]-1;j<2*n;j++)
    				{
    					if(man[j]==0)
    						cnt++;
    				
    				    
    				}
				
			
				
					if(cnt<n)
					System.out.println(-1);
				else
				{
				    int abc[] = new int[2*n];
				    for(int d=0;d<2*n;d++)
				    abc[d]=man[d];
				    int app=0;
					for(int j=0;j<n;j++)
					{
						app=0;
						for(int k=data[j];k<2*n;k++)
						{
						    
							if(abc[k]==0)
							{   app++;
								abc[k]=1;
								break;
							}
							
						}
						if(app==0)
							break;
					}
					if(app==0)
				    	System.out.println(-1);
					else
					{
    					for(int j=0;j<n;j++)
    					{
    						
    						for(int k=data[j];k<2*n;k++)
    						{
    							if(man[k]==0)
    							{  
    							    System.out.print(data[j]+" ");
    								System.out.print(k+1+" ");
    								man[k]=1;
    								break;
    							}
    						}
    					
    						
    					}System.out.println();
					}
				}
			}

		}
	}
}