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.*;

public class C {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        for (int r = 0; r < t; r++) {
            int n = in.nextInt();
            int[] b = new int[n];
            int[] a = new int[2 * n];
            TreeSet<Integer> set = new TreeSet<>();
            for (int i = 1; i <= 2 * n; i++) {
                set.add(i);
            }
            for (int i = 0; i < n; i++) {
                int x = in.nextInt();
                b[i] = x;
                a[(2 * i)] = x;
                set.remove(x);
            }
            boolean noE = true;
            for (int i = 0; i < n; i++) {
                try {
                    int x = set.higher(b[i]);
                    set.remove(x);
                    a[i * 2 + 1] = x;
                } catch (Exception e) {
                    noE = false;
                    System.out.println(-1);
                    break;
                }
            }
            if (noE) {
                for (int i : a) {
                    System.out.print(i + " ");
                }
                System.out.println();
            }

        }
    }
}