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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.StringTokenizer;

public class RestoringPermutation {
    public static void main(String[] args) {
        FastReader input=new FastReader();
        int t=input.nextInt();
        while(t-->0)
        {
            int n=input.nextInt();
            LinkedList<Integer> b=new LinkedList<>();
            HashSet<Integer> set=new HashSet<>();
            LinkedList<Integer> list=new LinkedList<>();
            for(int i=0;i<2*n;i++)
            {
                list.add(i+1);
            }
            int flag=0;
            for(int i=0;i<n;i++)
            {
                int v=input.nextInt();
                b.add(v);
                if(set.contains(v))
                {
                    flag=1;
                }
                else
                {
                    set.add(v);
                    list.remove((Object)v);
                }
            }
            if(flag==1)
            {
                System.out.println(-1);
            }
            else
            {
                int i=0;
                int f=0;
                while(i<2*n)
                {
                    int g=next(list,b.get(i));
                    if(g==-1)
                    {
                        f=1;
                        break;
                    }
                    else {
                        b.add(i + 1, list.get(g));
                        list.remove(g);
                        i += 2;
                    }
                }
                if(f==1)
                {
                    System.out.println(-1);
                }
                else
                {
                    for(int j=0;j<b.size();j++)
                    {
                        System.out.print(b.get(j)+" ");
                    }
                    System.out.println();
                }
            }

        }

    }
    public static int next(LinkedList<Integer> arr, int target)
    {
        int start = 0, end = arr.size() - 1;

        int ans = -1;
        while (start <= end) {
            int mid = (start + end) / 2;
            if (arr.get(mid) <= target) {
                start = mid + 1;
            }
            else {
                ans = mid;
                end = mid - 1;
            }
        }
        return ans;
    }
    static 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;
        }
    }
}