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.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int t= in.nextInt();
        while(t-- > 0) {
            boolean num[] = new boolean[12345];
            num[0] = true;

            int n = in.nextInt();
            int b[] = new int[n + 1];
            int a[] = new int[2*n + 1];

            for (int i = 0; i < n; i++) {
                b[i] = in.nextInt();
                num[b[i]]= true;
            }

            List<Integer> list = new ArrayList<>();

            for (int i = 0; i < n; i++) {
                list.add(b[i]);

                for (int j = b[i]+1; j < 300; j++) {
                    if(!num[j]) {
                        num[j] = true;
                        list.add(j);
                        break;
                    }
                }
            }

            List<Integer> answer = new ArrayList<>(list);
            Collections.sort(list);
            boolean flag = true;

            for (int i = 0; i < 2 * n; i++) {
                if(list.get(i) != i+1) {
                    flag = false;
                    break;
                }
            }

            StringBuilder sb = new StringBuilder();

            if(flag) {
                for (int i = 0; i < 2 * n; i++) {
                    sb.append(answer.get(i)).append(" ");
                }
                out.println(sb.toString());
            } else
                out.println(-1);
        }
        out.close();
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }

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