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.nio.CharBuffer;
import java.util.NoSuchElementException;

public class P1315C {

    public static void main(String[] args) {
        SimpleScanner scanner = new SimpleScanner(System.in);
        PrintWriter writer = new PrintWriter(System.out);

        int caseNum = scanner.nextInt();
        while (caseNum-- > 0) {
            int n = scanner.nextInt();
            boolean[] used = new boolean[2 * n + 1];
            int[] b = new int[n];
            for (int i = 0; i < n; ++i) {
                b[i] = scanner.nextInt();
                used[b[i]] = true;
            }
            boolean possible = true;
            int[] ans = new int[2 * n];
            for (int i = 0; i < n; ++i) {
                ans[i * 2] = b[i];
                boolean find = false;
                for (int j = b[i] + 1; j <= 2 * n; ++j) {
                    if (!used[j]) {
                        used[j] = true;
                        ans[i * 2 + 1] = j;
                        find = true;
                        break;
                    }
                }
                if (!find) {
                    possible = false;
                    break;
                }
            }
            if (possible) {
                for (int i = 0; i < 2 * n; ++i)
                    writer.print(ans[i] + " ");
                writer.println();
            } else
                writer.println(-1);
        }

        writer.close();
    }

    private static class SimpleScanner {

        private static final int BUFFER_SIZE = 10240;

        private Readable in;
        private CharBuffer buffer;
        private boolean eof;

        private SimpleScanner(InputStream in) {
            this.in = new BufferedReader(new InputStreamReader(in));
            buffer = CharBuffer.allocate(BUFFER_SIZE);
            buffer.limit(0);
            eof = false;
        }


        private char read() {
            if (!buffer.hasRemaining()) {
                buffer.clear();
                int n;
                try {
                    n = in.read(buffer);
                } catch (IOException e) {
                    n = -1;
                }
                if (n <= 0) {
                    eof = true;
                    return '\0';
                }
                buffer.flip();
            }
            return buffer.get();
        }

        private void checkEof() {
            if (eof)
                throw new NoSuchElementException();
        }

        private char nextChar() {
            checkEof();
            char b = read();
            checkEof();
            return b;
        }

        private String next() {
            char b;
            do {
                b = read();
                checkEof();
            } while (Character.isWhitespace(b));
            StringBuilder sb = new StringBuilder();
            do {
                sb.append(b);
                b = read();
            } while (!eof && !Character.isWhitespace(b));
            return sb.toString();
        }

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

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

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