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.*;

public class Main
{ 
    static BufferedReader br;
    static StringTokenizer st;
    static PrintWriter pr = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    
    public static class HS<T> extends HashSet<T> {};

    public static void main(String[] args) throws IOException 
	{
		br = new BufferedReader(new InputStreamReader(System.in));
		st = new StringTokenizer(br.readLine());
		int t = nxtInt();
		
		while(t-- > 0)
		{
		    st = new StringTokenizer(br.readLine());
		    int n = nxtInt();
		    int[] a = new int[n*2];
		    HS<Integer> mrk = new HS<>();
    		
    		st = new StringTokenizer(br.readLine());
    		for(int i=0; i<n; i++) 
    		{
    		    a[i*2] = nxtInt();
    		    mrk.add(a[i*2]);
    		}
    		
    		boolean flg = true;
    		StringBuilder ans = new StringBuilder();
    		for(int i=1; i<a.length; i+=2) 
    		{
    		    int num = a[i-1];
    		    while(num<n*2+1 && mrk.contains(num)) num++;
    		    
    		    if(num > n*2)
    		    {
    		        flg = false;
    		        break;
    		    }
    		    a[i] = num;
    		    mrk.add(num);
    		    ans.append(a[i-1] + " "  + a[i] + " ");
    		}
    		
            pr.println(flg? ans: -1);
		}
		
		pr.flush();
		pr.close();
    }
    
    static int nxtInt(){
        return Integer.parseInt(nxt());
    }
    
    static long nxtLong(){
        return Long.parseLong(nxt());
    }
    
    static double nxtDoub(){
        return Double.parseDouble(nxt());
    }
    
    static String nxt(){
        return st.nextToken();
    }
    
    static String nxtLn() throws IOException{
        return br.readLine();
    }
}