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.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;



import java.lang.Math;

public class Test {

	public static void main(String[] args) {
		
		Scanner s = new Scanner(System.in);
		
		int t=s.nextInt();
		
		for(int i=0;i<t;i++)
		{
			
			int n=s.nextInt();
			List<Integer> r1 = new ArrayList<Integer>();
			List<Integer> r2 = new ArrayList<Integer>();
			List<Integer> r3 = new ArrayList<Integer>();
			
			for(int j=0;j<n;j++)
			{
				r1.add(s.nextInt());
			}
			
			for(int j=1;j<2*n+1;j++)
			{
				if(!r1.contains(j))
					r2.add(j);
			}
			
			Collections.sort(r2);
			int count=0;
			boolean bool=true;
			

			while(!r1.isEmpty())
			{
				boolean came=false;
				for(int j=0;j<r2.size();j++)
				{
					
					if(r2.get(j)>r1.get(0))
					{
						r3.add(r1.get(0));
						r3.add(r2.get(j));
						
						r1.remove(0);
						r2.remove(j);
						
						came=true;
						break;
					}
					
				}
				
				if(came==true)
					continue;
				
				
				
				System.out.println(-1);
				bool=false;
				break;
				
				
			}
			
			if(bool==true)
			{
				for(int j=0;j<2*n;j++)
				{
					System.out.print(r3.get(j)+" ");
				}
				System.out.println();
			}
			
			
		}
	}

}