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.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.TreeSet;
import java.io.InputStream;

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

    static class CRestoringPermutation {
        public void solve(int testNumber, FastReader sc, PrintWriter out) {

            int t = sc.nextInt();
            while (t-- > 0) {
                int n = sc.nextInt();
                int[] b = new int[n];
                for (int i = 0; i < n; ++i) b[i] = sc.nextInt();
                n = 2 * n;
                int[] a = new int[n];
                TreeSet<Integer> tree = new TreeSet<>();
                for (int i = 1; i <= n; ++i) tree.add(i);
                int ptr = 0;
                for (int i = 0; i < n; i += 2) {
                    a[i] = b[ptr++];
                    tree.remove(a[i]);
                }

                boolean yes = false;
                for (int i = 1; i < n && !yes; i += 2) {
                    int x = a[i - 1];
                    if (tree.higher(x) == null)
                        yes = true;
                    else {
                        a[i] = tree.higher(x);
                        tree.remove(a[i]);
                    }
                }
                if (yes) out.print(-1);
                else for (int i = 0; i < a.length; ++i) out.print(a[i] + " ");
                out.println();
            }
        }

    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader(InputStream stream) {
            br = new BufferedReader(new
                    InputStreamReader(stream), 32768);
        }

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

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

    }
}