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.lang.reflect.Array;
import java.util.*;
import java.awt.Point;

public class Main {
    static int mod=(int)1e9+7;
    public static void main(String[] args) throws Exception {
        FastReader sc = new FastReader();
        StringBuilder sb=new StringBuilder();
        int t=sc.nextInt();
        while(t-->0){
            int n=sc.nextInt();
            int[] b=new int[n];
            boolean[] c=new boolean[2*n+1];
            for(int i=0;i<n;i++)c[b[i]=sc.nextInt()]=true;
            TreeSet<Integer> treeSet=new TreeSet<>();
            for(int i=1;i<=2*n;i++){
                if(!c[i])treeSet.add(i);
            }
            StringBuilder temp=new StringBuilder();
            boolean z=false;
            for(int i=0;i<n;i++){
                Integer x=treeSet.higher(b[i]);
                if(x==null){
                    z=true;
                    break;
                }
                temp.append(b[i]+" "+x+" ");
                treeSet.remove(x);
            }
            if(z)sb.append("-1\n");
            else sb.append(temp+"\n");
        }
        System.out.println(sb);
    }
//    static boolean gcd(int a,int b){
//        if(b==0)return a==1;
//        else return gcd(b,a%b);
//    }
}

class FastReader {
    BufferedReader br;
    StringTokenizer st;

    public FastReader() {
        br = new BufferedReader(new
                InputStreamReader(System.in));
    }

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

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

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

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

    String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}