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.io.*;
import static java.lang.Math.*;

public class Main implements Runnable
{
    boolean multiple = true;
    long MOD;

    @SuppressWarnings("Duplicates")
    void solve() throws Exception
    {
        int n = sc.nextInt();
        TreeSet<Integer> remaining = new TreeSet<>();
        for (int i = 1; i <= 2 * n; i++)
            remaining.add(i);
        int[] arr = new int[n];
        int[] ans = new int[n];
        for (int i = 0; i < n; i++)
        {
            int next = sc.nextInt();
            remaining.remove(next);
            arr[i] = next;
        }

        for (int i = 0; i < n; i++)
        {
            Integer next = remaining.higher(arr[i]);
            if (next == null)
            {
                System.out.println(-1);
                return;
            }

            ans[i] = next;
            remaining.remove(next);
        }

        for (int i = 0; i < n; i++)
            System.out.print(arr[i] + " " + ans[i] + " ");
        System.out.println();
    }

    class Node implements Comparable<Node>
    {
        long t, u, v;
        Node(long T, long U, long V)
        {
            t = T;
            u = U;
            v = V;
        }

        @Override
        public int compareTo(Node o)
        {
            return (int)(t - o.t);
        }
    }

    long inv(long a, long b)
    {
        return 1 < a ? b - inv(b % a, a) * b / a : 1;
    }

    long gcd(long a, long b)
    {
        return a == 0 ? b : gcd(b % a, a);
    }

    long lcm(long a, long b) { return (a * b) / gcd(a , b); }

    class SegNode
    {
        int max;
        int L, R;
        SegNode left = null, right = null;

        int query(int queryL, int queryR)
        {
            if (queryL == L && queryR == R)
                return max;

            int leftAns = Integer.MIN_VALUE, rightAns = Integer.MIN_VALUE;
            if (left != null && queryL <= left.R)
                leftAns = left.query(queryL, min(queryR, left.R));
            if (right != null && queryR >= right.L)
                rightAns = right.query(max(queryL, right.L), queryR);

            return max(leftAns, rightAns);
        }

        SegNode(int[] arr, int l, int r)
        {
            L = l;
            R = r;
            max = arr[l];

            if (l == r) return;

            int mid = (l + r) / 2;
            left = new SegNode(arr, l, mid);
            right = new SegNode(arr, mid + 1, r);
            max = max(left.max, right.max);
        }
    }

    void print(long[] arr)
    {
        for (int i = 0; i < arr.length; i++)
            System.out.print(arr[i] + " ");
        System.out.println();
    }

    @Override
    public void run()
    {
        try
        {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            sc = new FastScanner(in);
            if (multiple)
            {
                int q = sc.nextInt();
                for (int i = 0; i < q; i++)
                    solve();
            }
            else
                solve();
        }
        catch (Throwable uncaught)
        {
            Main.uncaught = uncaught;
        }
        finally
        {
            out.close();
        }
    }

    public static void main(String[] args) throws Throwable
    {
        Thread thread = new Thread(null, new Main(), "", (1 << 26));
        thread.start();
        thread.join();
        if (Main.uncaught != null) {
            throw Main.uncaught;
        }
    }

    static Throwable uncaught; BufferedReader in; FastScanner sc; PrintWriter out;
}

class FastScanner
{
    BufferedReader in;
    StringTokenizer st;

    public FastScanner(BufferedReader in)
    {
        this.in = in;
    }

    public String nextToken() throws Exception {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }

    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
}