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.swing.*;
    import java.awt.desktop.SystemSleepEvent;
    import java.util.*;
    import java.io.*;


    public class Main {
        public static class FastReader {
            BufferedReader br;
            StringTokenizer st;

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

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

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

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

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

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


        }
        public class pair {
            int a;
            int b;

            pair(int p, int q) {
                a = p;
                b = q;
            }
            public int hashCode() {
                return new Integer(a).hashCode() * 31 + new Integer(b).hashCode();
            }
        }

        public static int gcd(int a, int b) {
            if (a == 1 || b == 1)
                return 1;
            if (a == 0)
                return b;
            if (b == 0)
                return a;
            return gcd(b % a, a);
        }






        public static void main(String[] args) {
            FastReader s = new FastReader();
            int t=s.nextInt();
            while(t>0)
            {
                int n=s.nextInt();
                int[] arr=new int[n];
                int[] arr1=new int[2*n];
                for(int i=0;i<n;i++)
                {
                    arr[i] = s.nextInt();
                }
                for(int i=0;i<2*n;i++)
                    arr1[i]=i+1;
                int[] dif=new int[1000];
                int c=0;
                for(int i=0;i<2*n;i++)
                {
                    int temp = arr1[i];
                    if(!find(arr,temp))
                    {
                        dif[c] = temp;
                        c++;
                    }
                }
                // System.out.println(c);
                int min=arr[0];
                for(int i=0;i<n;i++)
                {
                    if(arr[i]<=min)
                        min=arr[i];
                }
                int av=greater(dif,min);
                //System.out.println();
                //System.out.println(av);
                if(av<n)
                {
                    System.out.println(-1);
                }
                else
                {
                    int[] visited=new int[n];
                    int[] ans=new int[2*n];
                    int temp1=0;
                    int ct=0;
                    int flag=0;
                    for(int i=0;i<2*n-1;i++)
                    {
                        ans[i] = arr[ct];
                        int x = ans[i];

                        for(int j=0;j<c;j++)
                        {
                            if(dif[j]>x && visited[j]!=1)
                            {
                                flag=1;
                                temp1=j;
                                break;
                            }
                        }
                        if(flag==0)
                            break;
                        else
                        {
                            ans[i+1] = dif[temp1];
                            visited[temp1]=1;
                            i++;
                            ct++;
                        }
                    }
                    if(flag==0)
                        System.out.println(-1);
                    else
                    {
                        int flag1=0;
                        int[] b = new int[1000];
                        for(int i=0;i<2*n;i++)
                        {
                            b[ans[i]]++;
                            if(b[ans[i]]>1)
                            {
                                flag1=1;
                                break;
                            }
                        }
                        if(flag1==1)
                            System.out.println(-1);
                        else {
                            for (int i = 0; i < 2 * n; i++) {
                                System.out.print(ans[i] + " ");

                            }

                            System.out.println();
                        }
                    }
                }






                t--;
            }
        }

        public static boolean find(int[] arr, int x)
        {
            int n=arr.length;
            for(int i=0;i<n;i++)
            {
                if(arr[i]==x)
                    return true;
            }
            return false;
        }

        public static int greater(int[] arr, int x)
        {
            int n=arr.length;
            int temp=0;
            for(int i=0;i<n;i++)
            {
                if(arr[i]>x)
                {
                    temp=i;
                    break;
                }
            }
            return n-temp;

        }
    }