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:
// package com.company;
import java.util.*;
import java.lang.*;
import java.io.*;
//****Use Integer Wrapper Class for Arrays.sort()****
public class BV3 {
    public static void main(String[] Args){
        FastReader scan=new FastReader();
        int t=scan.nextInt();
        while(t-->0){
            int n=scan.nextInt();
            int[] arr=new int[n];
            Set<Integer> nu=new HashSet<>();
            for(int i=1;i<=2*n;i++){
                nu.add(i);
            }
            for (int i = 0; i <n ; i++) {
                arr[i]=scan.nextInt();
                nu.remove(arr[i]);
            }
            int[] tkn=new int[n];
            int[] ans=new int[2*n];
            boolean flag=true;
            for(int i=0;i<n;i++){
                ans[2*i]=arr[i];
                int nxt=500;
                for(Integer j:nu){
                    if(j>ans[2*i]&&j<nxt){
                        nxt=j;
                    }
                }
                if(nxt==500){
                    flag=false;
                    break;
                }
                else{
                    nu.remove(nxt);
                    ans[2*i+1]=nxt;
                }
            }
            if(!flag){
                System.out.println(-1);
            }
            else{
                for(int i=0;i<2*n;i++){
                    System.out.print(ans[i]+" ");
                }
                System.out.println();
            }
        }
    }
    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;
        }
    }

}