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.OutputStream;
import java.util.*;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.LinkedHashSet;
import java.io.Writer;
import java.io.OutputStreamWriter;
 
/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Egor Kulikov (egor@egork.net)
 */
 
public class Solution {
 
    public static void main(String[] args) {
 
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        Solutio solver = new Solutio();
        int testCount = Integer.parseInt(in.next());
        int sum=0,te=0;
 
        for (int i = 1; i <= testCount; i++) 
        {
            solver.solve(i, in, out);
        }
        out.close();
    }
//**********************SOLVE    HERE     EVERYTHING******************************
 
 
 
    //1 2 3 4 5 
    static class Solutio {
 
        public void solve(int testNumber, InputReader in, OutputWriter out) {
        	int n=in.readInt();
        	int arr[]=new int[n];
        	for(int i=0;i<n;i++)
        		arr[i]=in.readInt();
        	int arr2[]=new int[2*n],te=0,ch=0;
        	for(int i=0,k=0;i<n;i++,k+=2)
        	{
        		
        		arr2[k]=arr[i];
        		te=arr[i]+1;ch=0;
        		while(ch==0 && te<=2*n)
        		{
        			ch=1;
        			for(int j=0;j<2*i;j++)
        			{
        				if(arr2[j]==te) {
        					te++;ch=0;}
        			}
        			for(int l=0;l<n;l++)
        			{
        				if(arr[l]==te) {
        					te++;ch=0;}
        			}
        			
        		}
        		arr2[k+1]=te;
        		if(te>2*n)
        		{
        			System.out.println(-1);return;
        		}
        		
        		
        	}
        	//System.out.println(Arrays.toString(arr)+"  arr");
        	for(int i=0;i<2*n;i++)
        		System.out.print(arr2[i]+" ");
        	System.out.println();
        	
        
        	
        }       
    }
 
 
//*********************END        HERE       EVERYTHING*******************************    
 
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;
 
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
 
        public void readIntArrays(int[]... arrays) {
            for (int i = 0; i < arrays[0].length; i++) {
                for (int j = 0; j < arrays.length; j++) {
                    arrays[j][i] = readInt();
                }
            }
        }
 
        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }
 
        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }
 
        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        public String next() {
            return readString();
        }
 
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
 
        }
 
    }
 
    static class OutputWriter {
        private final PrintWriter writer;
 
        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }
 
        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }
 
        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }
 
        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }
 
        public void close() {
            writer.close();
        }
 
    }
 
 
}