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.util.*;
public class Main {
    private static void solver(InputReader sc, PrintWriter out) throws Exception {
      int test  = sc.nextInt();
      for(int ii=0; ii<test; ii++){
          int n = sc.nextInt();
          Set<Integer> hs = new HashSet<>();
          int arr[] = new int[n];
          for(int i=0; i<n; i++){
              int x = sc.nextInt();
              hs.add(x);
              arr[i] = x;
          }
          List<Integer> al = new ArrayList<>();
          boolean ans = true;
          for(int xx : arr){
              int max = xx+1;
              while(true){
                  if(hs.contains(max)) max++;
                  else break;
              }
          //    out.println(max);
              if(max > (2 * n)){
                  ans = false; break;
              }
              al.add(xx); al.add(max); hs.add(max);
          }
          if(!ans) out.println(-1);
          else{
              for(int xx : al) out.print(xx+" ");
              out.println();
          }
      }
    }
    private static long gcd(long a, long b){
        if(b==0) return a;
        return  gcd(b, a%b);
    }
    public static void main(String[] args) throws Exception {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        solver(in,out);
        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());
        }
        public double nextDouble(){
            return Double.parseDouble(next());
        }
    }
}
class Pair{
    int x,y,z;
    Pair(int x, int y, int z){
        this.x = x;this.y = y;
        this.z = z;
    }
}