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:
/*input
5
1
1
2
4 1
3
4 1 3
4
2 3 4 5
5
1 5 7 2 8
*/


import java.math.*;
import java.io.*;
import java.util.*;
public class Main
{
    static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead;
public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        }
public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        }
public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        }
public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9');
if (neg) 
                return -ret; 
            return ret; 
        }
public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        }
public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read();
do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9');
if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            }
if (neg) 
                return -ret; 
            return ret; 
        }
private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        }
private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        }
public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    } 





    static Reader sc=new Reader();
    static BufferedWriter bw=new BufferedWriter(new OutputStreamWriter(System.out));
    public static void main(String args[])throws IOException
    {
        /*
         * For integer input: int n=inputInt();
         * For long input: long n=inputLong();
         * For double input: double n=inputDouble();
         * For String input: String s=inputString();
         * Logic goes here
         * For printing without space: print(a+""); where a is a variable of any datatype
         * For printing with space: printSp(a+""); where a is a variable of any datatype
         * For printing with new line: println(a+""); where a is a variable of any datatype
         */

int t=inputInt();
while(t>0){

int n=inputInt();

HashSet<Integer> hs = new HashSet<>();
List<Integer> ls = new ArrayList<>();
int min=2*n,max=0;
for(int i=0;i<n;i++)
{
	int x=inputInt();
	ls.add(x);
	if(x<2*n)
	hs.add(x);
if(x<min)
	min=x;
if(x>max)
	max=x;
}

if(hs.size()==n && min==1 && max<2*n)
{
	String s="";
	int flag=0;
	for(int i=0;i<n;i++)
	{
		int x=ls.get(i)+1;
		while(hs.contains(x))
		{
			x++;
		}

		if(x>2*n)
		{
			flag=1;
			break;
		}
		s+=ls.get(i)+" "+x+" ";
		hs.add(x);
	}

	if(flag==0)
	println(s+"");
else
	println("-1");
}
else
println("-1");


t--;
}
 
       bw.flush();
        bw.close();
}
        

     public static int inputInt()throws IOException
    {
        return sc.nextInt();
    }
    public static long inputLong()throws IOException
    {
        return sc.nextLong();
    }
    public static double inputDouble()throws IOException
    {
        return sc.nextDouble();
    }
    public static String inputString()throws IOException
    {
        return sc.readLine();
    }
    public static void print(String a)throws IOException
    {
        bw.write(a);
    }
    public static void printSp(String a)throws IOException
    {
        bw.write(a+" ");
    }
    public static void println(String a)throws IOException
    {
        bw.write(a+"\n");
    }
}