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 javafx.util.Pair;
import org.omg.CORBA.INTERNAL;
import sun.awt.image.ImageWatched;
import sun.reflect.generics.tree.Tree;

import java.nio.channels.ScatteringByteChannel;
import java.text.SimpleDateFormat;
import java.util.*;

public class Main {



        public static void main(String[] args) {


            Scanner s = new Scanner(System.in);

            int tc = s.nextInt();

            tc:for (int t = 0; t < tc; t++) {


                int n = s.nextInt();

                int boundary = 2*n;
                boolean[] flag = new boolean[boundary + 1];


                int[] answer = new int[2*n];

                int seq[] = new int[n];

                for (int i = 0; i < n; i++) {

                    seq[i] = s.nextInt();

                    flag[seq[i]] = true;

                }

                local:for (int i = 0; i < n; i++) {

                    int num = seq[i];

                    if (num >= boundary)  {

                        System.out.println(-1);

                        continue  tc;
                    }
                    answer[2*i] = num;


                    for (int j = num+1; j < 2*n+1; j++) {

                        if (flag[j] == false) {

                            flag[j] = true;

                            answer[2*i+1] = j;

                            continue  local;
                        }


                    }

                    System.out.println(-1);

                    continue tc;

                }

                for (int k : answer) {

                    System.out.print(k + " ");
                }

                System.out.print("\n");
            }

        }
    }