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:
//package Practise;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Random;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class RestoringPermutation {
	public static void main(String args[]) {
		FastScanner fs=new FastScanner();
		int t=fs.nextInt();
		for(int t1=0;t1<t;t1++) {
			int n=fs.nextInt();
			int []arr=new int[n];
			boolean []check=new boolean[2*n+1];
			for(int i=0;i<n;i++) {
				arr[i]=fs.nextInt();
				check[arr[i]]=true;
			}
			TreeSet<Integer> set=new TreeSet<>();
			for(int i=1;i<check.length;i++) {
				if(!check[i])
					set.add(i);
			}
			List<Integer> list=new ArrayList<>();boolean flag=false;
			for(int i=0;i<arr.length;i++) {
				list.add(arr[i]);
				Integer val=set.higher(arr[i]);
				flag=val==null?true:false;
				if(flag)
					break;
				list.add(val);
				set.remove((Object)val);
					
			}
			if(flag)
				System.out.println("-1");
			else {
				for(int val:list)
					System.out.print(val+" ");
				System.out.println();
			}
		}
	}
	private static int[] readArray(int n) {
		// TODO Auto-generated method stub
		return null;
	}

static final Random random=new Random();
	
	static void ruffleSort(int[] a) {
		int n=a.length;//shuffle, then sort 
		for (int i=0; i<n; i++) {
			int oi=random.nextInt(n), temp=a[oi];
			a[oi]=a[i]; a[i]=temp;
		}
		Arrays.sort(a);
	}
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
}
}