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 CodeForces;

import java.io.*;
import java.nio.file.Paths;
import java.util.Scanner;

public class Solution {
    private static final boolean onlineJudge = "true".equals(System.getProperty("ONLINE_JUDGE"));
    
    public static void main(String[] args) throws IOException {
        FileInputStream fileStream = null;
        Scanner scanner = new Scanner(onlineJudge ? System.in : (fileStream = new FileInputStream(Paths.get(System.getProperty("user.dir"), "src/res/input").toString())));
        int t = scanner.nextInt();
        while (t-- > 0) {
            int n = scanner.nextInt();
            boolean[] f = new boolean[n << 1];
            int[] a = new int[n << 1];
            int[] b = new int[n];
            for (int i = 0; i < n; i++) {
                b[i] = scanner.nextInt();
                f[b[i] - 1] = true;
            }
            boolean exist = true;            
            for (int i = 0; i < n; i++) {
                a[i << 1] = b[i];
                f[b[i] - 1] = true;
                if(b[i] == n << 1) {
                    exist = false;
                    break;
                }
                int max = -1;
                for (int j = b[i]; j < n << 1; j++) {
                    if(!f[j]) {
                        max = j + 1;
                        f[j] = true;
                        break;
                    }
                }
                if(max == -1) {
                    exist = false;
                    break;
                }
                a[(i << 1) + 1] = max;
            }
            if(exist) {
                for(int j = 0; j < a.length; j++) {
                    System.out.print(a[j]);
                    if (j == a.length - 1) {
                        System.out.print("\n");
                    } else {
                        System.out.print(" ");
                    }
                }
            }
            else {
                System.out.println(-1);
            }
        }
        if(fileStream != null) {
            fileStream.close();
        }
        
        scanner.close();
    }
}