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.*;
import java.util.stream.Collectors;

public class RestoringPermutation {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int test = scanner.nextInt();
        scanner.nextLine();

        for (int t = 0; t < test; t++) {
            int n = scanner.nextInt();
            scanner.nextLine();

            int[]arr = new int[n];
            Set<Integer> nums = new HashSet<>();
            for (int i = 0; i < n; i++) {
                arr[i] = scanner.nextInt();
                nums.add(arr[i]);
            }
            scanner.nextLine();


            TreeSet<Integer> remaining = new TreeSet<>();
            for (int i = 1; i < 2 * n + 1; i++) {
                if (!nums.contains(i)) {
                    remaining.add(i);
                }
            }

            int[] result = new int[2 * n];
            boolean invalid = false;
            for (int i = 0; i < n; i++) {
                int num1 = arr[i];
                Integer ceiling = remaining.ceiling(num1);

                if (ceiling != null) {
                    result[2 * i] = num1;
                    result[2 * i + 1] = ceiling;
                    remaining.remove(ceiling);
                }else{
                    invalid = true;
                    break;
                }
            }

            if (invalid) {
                System.out.println(-1);
            }else{
                System.out.println(Arrays.stream(result).mapToObj(e -> String.valueOf(e)).collect(Collectors.joining(" ")));
            }
        }
    }
}