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 javax.management.DynamicMBean;
import javax.print.DocFlavor;
import javax.print.attribute.HashAttributeSet;
import java.awt.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.nio.file.attribute.FileAttribute;
import java.time.DayOfWeek;
import java.time.LocalDate;
import java.time.Month;
import java.time.temporal.TemporalAdjusters;
import java.util.List;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.*;
import java.util.Arrays;
import java.util.concurrent.Callable;
import java.time.DayOfWeek;
import java.time.LocalDate;
import java.time.Month;
import java.time.temporal.TemporalAdjusters;



public class Main {


    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static void main(String[] args) {
        FastReader sc = new FastReader();

        int t=sc.nextInt();
        for(int i=0;i<t;i++){
           int n=sc.nextInt();
           int[] arr=new int[n];
            HashSet<Integer> set=new HashSet<>();

            for(int j=0;j<n;j++){
               arr[j]=sc.nextInt();
               set.add(arr[j]);
           }
            int p=0,q=0;
           int[] a=new int[2*n];
           int flag=1,index=0;
           for(int j=0;j<n;j++){
                p=arr[j];
                q=p+1;
                if(q>2*n){
                    flag=0;
                    break;
                }
                while(set.contains(q)){
                    q++;
                    if(q>2*n)
                    {
                        flag=0;
                        break;
                    }
                }
                if(flag==0){
                    break;
                }
                set.add(q);
                a[index]=p;
                a[index+1]=q;
                index+=2;
           }
           if(flag==0){
               System.out.print(-1);
           }
           else{
               for(int j=0;j<2*n;j++){
                   System.out.print(a[j]+" ");
               }
           }
           System.out.println(" ");

        }
    }
}