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.util.Scanner;
import java.util.TreeSet;

public class Solution {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int tc = sc.nextInt();
        while(tc-- > 0) {
            int n = sc.nextInt();
            TreeSet<Integer> set = new TreeSet<>();
            for(int i = 1; i<=2*n; i++) {
                set.add(i);
            }
            int[] a = new int[n];
            for(int i = 0; i<n; i++) {
                int ai = sc.nextInt();
                set.remove(ai);
                a[i] = ai;
            }
            int[] b = new int[2*n];
            boolean foundAns = true;
            for(int i = 0; i<n; i++) {
                Integer ceiling = set.ceiling(a[i]);
                if(ceiling != null) {
                    b[2*i] = a[i];
                    b[2*i + 1] = ceiling;
                    set.remove(ceiling);
                } else {
                    foundAns = false;
                    break;
                }
            }
            if(foundAns) {
                for(int i = 0; i<2*n; i++)
                    System.out.print(b[i] + " ");
                System.out.println();
            } else {
                System.out.println(-1);
            }

        }

    }
}