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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Vector;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.util.Collections;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author xwchen
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int t = in.nextInt();
            while (t-- > 0) {
                int n = in.nextInt();
                int[] b = new int[n + 1];
                int[] pos = new int[2 * n + 1];
                int[] a = new int[2 * n + 1];
                boolean[] occur = new boolean[n * 2 + 1];
                for (int i = 1; i <= n; ++i) {
                    b[i] = in.nextInt();
                    occur[b[i]] = true;
                    pos[b[i]] = 2 * i - 1;
                }
                Vector<Integer> others = new Vector<>();
                for (int i = 1; i <= 2 * n; ++i) {
                    if (!occur[i]) {
                        others.add(i);
                    }
                }
                Collections.sort(others);
                Arrays.sort(b, 1, n + 1);
                boolean OK = true;
                for (int i = 1; i <= n; ++i) {
                    int other = others.get(i - 1);
                    if (b[i] > others.get(i - 1)) {
                        OK = false;
                        break;
                    } else {
                        pos[other] = pos[b[i]] + 1;
                    }
                }
                if (!OK) {
                    out.println(-1);
                    continue;
                }
                for (int i = 1; i <= 2 * n; ++i) {
                    a[pos[i]] = i;
                }

                boolean move = false;
                do {
                    move = false;
                    for (int i = 2; i <= 2 * n; i += 2) {
                        for (int j = i + 2; j <= 2 * n; j += 2) {
                            int p = i;
                            int q = j;
                            if (a[p] > a[q] && a[p - 1] < a[q] && a[q - 1] < a[p]) {
                                int tmp = a[p];
                                a[p] = a[q];
                                a[q] = tmp;
                                move = true;
                            }
                        }
                    }
                } while (move);


                for (int i = 1; i <= 2 * n; ++i) {
                    out.print(a[i] + " ");
                }


                out.println();
            }
        }

    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer tokenizer = new StringTokenizer("");

        public InputReader(InputStream inputStream) {
            this.reader = new BufferedReader(
                    new InputStreamReader(inputStream));
        }

        public String next() {
            while (!tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}