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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Collections;
import java.util.TreeSet;

public class Permutation {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        PrintWriter out = new PrintWriter(System.out);
        StringBuilder k = new StringBuilder("");
        while(t-->0){
            int n = Integer.parseInt(br.readLine());
            String[] arr = br.readLine().split(" ");
            int b[] = new int[n];
            int[] c = new int[n];
            TreeSet<Integer> s1 = new TreeSet<>();
            for(int i=1;i<=2*n;i++){
                s1.add(i);
            }
            for(int i=0;i<n;i++){
                b[i] = Integer.parseInt(arr[i]);
                c[i]=b[i];
                s1.remove(b[i]);
            }
            boolean isPossible = true;
            Arrays.sort(b);
            for(int j=0;j<n;j++){
                if(b[j]>=(j+1)*2){
                    isPossible = false;
                    break;
                }
            }
            if(!isPossible) {
                k.append(-1 + "\n");
            }else{
                for(int i=0;i<n;i++){
                    if(i!=0){
                        k.append(" ");
                    }
                    k.append(c[i]+" "+getNextGreater(c[i], s1));
                }
                k.append("\n");
            }
        }
        out.print(k);
        out.flush();
    }

    private static int getNextGreater(int i, TreeSet<Integer> s1) {
        for(int p:s1){
            if(p>i){
                s1.remove(p);
                return p;
            }
        }
        return 0;
    }


}