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.*;
import java.math.*;
import java.util.*;

public class Solve {
    FastScanner in;
    PrintWriter out;

    void solve() {
        int T = in.nextInt();
        while (0 < T--) {
            int n = in.nextInt();
            int[] b = in.nextIntArray(n);
            HashSet<Integer> hs = new HashSet<>();
            boolean[] used = new boolean[n*2+1];
            for (int i = 0; i < n; i++) {
                used[b[i]] = true;
            }
            int[] a = new int[n*2];
            Arrays.fill(a, -1);
            for (int i = 0; i < n; i++) {
                a[i*2] = b[i];
                int tmp = b[i]+1;
                while (tmp <= n*2 && used[tmp]) {
                    tmp++;
                }
                if (tmp <= n*2 && ! used[tmp]) {
                    a[i*2+1] = tmp;
                    used[tmp] = true;
                }
            }

            boolean ok = true;
            for (int i = 0; i < n*2; i++) {
                if (a[i] == -1) {
                    ok = false;
                    break;
                }
            }

            if (ok) {
                for (int i = 0; i < n*2; i++) {
                    out.print(a[i] + " ");
                }
                out.println();
            } else {
                out.println(-1);
            }

            // out.println(Arrays.toString(a));

            // 4   1
            // -1

            // bi = min(a2i-1, a2i)


            // 1
            // 1 2



            // 4   1   3      b   n=3
            // 4 5 1 2 3 6    a  2n=6
            // * *
            //     * *
            //         * *



            // 1   5   7   2   8
            // 1 3 5 6 7 9 2 4 8 10
        }
    }

    void run() {
        try {
            in = new FastScanner(new File("Solve.in"));
            out = new PrintWriter(new File("Solve.out"));

            solve();

            out.close();
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }

    void runIO() {

        in = new FastScanner(System.in);
        out = new PrintWriter(System.out);

        solve();

        out.close();
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return null;
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

        boolean hasMoreTokens() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return false;
                st = new StringTokenizer(s);
            }
            return true;
        }

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

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
            }
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.nextLong();
            }
            return a;
        }

        BigInteger nextBigInteger() {
            return new BigInteger(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        double[] nextDoubleArray(int n) {
            double[] a = new double[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.nextDouble();
            }
            return a;
        }

    }

    public static void main(String[] args) {
        new Solve().runIO();
    }
}