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.ArrayList;
import java.util.HashMap;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		FastReader s = new FastReader();
		int tc = s.nextInt();
		while(tc-- > 0) {
			int n = s.nextInt();
			int[] input = new int[n];
			boolean[] taken = new boolean[2*n + 1];
			for(int i = 0;i < n;i++) {
				input[i] = s.nextInt();
				taken[input[i]] = true;
			}
			ArrayList<Integer> arr = new ArrayList<>();
			int i = 0;
			for(i = 0;i < n;i++) {
				int val = nextGreater(input[i] ,  taken);
				if(val == -1) {
					System.out.println("-1");
					break;
				}
				arr.add(input[i]);
				arr.add(val);
			}
			if(i == n) {
				for(int j : arr) System.out.print(j + " ");
				System.out.println();
			}
			
		}
	}
	public static int nextGreater(int val , boolean[] taken) {
		int n = taken.length/2;
		for(int i = val + 1;i <= 2*n;i++) {
			if(!taken[i]) {
				taken[i] = true;
				return i;
			}
		}
		return -1;
	}
}

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; 
	} 
}