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.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.*;

public class ProblemC {

    public static InputStream inputStream = System.in;

    public static OutputStream outputStream = System.out;

    public static void main(String[] args) {
        Scanner scanner = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);

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

            List<Integer> list = new ArrayList<>();
            List<Integer> ans = new ArrayList<>();
            List<Integer> aList = getAList(n);
            for (int i = 0; i < n; i++) {
                int x = scanner.nextInt();
                list.add(x);
                aList.remove(new Integer(x));
            }

            boolean cant = false;
            for (int i = 0; i < n; i++) {
                int x = list.get(i);
                int y = getSmallest(x, aList);
                if (y == -1) {
                    out.println(-1);
                    cant = true;
                    break;
                }
                ans.add(x);
                ans.add(y);
            }

            if (!cant) {
                for (int x : ans) {
                    out.print(x + " ");
                }
                out.println();
            }
            out.flush();
        }

        out.flush();
    }

    private static int getSmallest(int x, List<Integer> list) {
        for (int a : list) {
            if (a > x) {
                list.remove(new Integer(a));
                return a;
            }
        }
        return -1;
    }

    private static List<Integer> getAList(int n) {
        List<Integer> list = new ArrayList<>();
        for (int i = 1; i <= 2 * n; i++) {
            list.add(i);
        }
        return list;
    }
}