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.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeSet;
 
public class zz {
 
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);
		int t = Integer.parseInt(br.readLine());
		while (t-- > 0) {
			int n = Integer.parseInt(br.readLine());
			StringTokenizer st = new StringTokenizer(br.readLine());
			int b[] = new int[n];
			int a[] = new int[2 * n];
			TreeSet<Integer> ts = new TreeSet<>();
			for (int i = 0; i < a.length; i++) {
				ts.add(i + 1);
			}
			for (int i = 0; i < b.length; i++) {
				b[i] = Integer.parseInt(st.nextToken());
				a[2*i]=b[i];
				ts.remove(b[i]);
			}
			boolean f=true;
			for (int i = 0; i < b.length; i++) {
				if(ts.ceiling(b[i])==null) {
					f=false;
					break;
				}
				a[2*i+1]=ts.ceiling(b[i]);
				ts.remove(a[2*i+1]);
			}
		if(f) {
			for(int e:a)
				System.out.print(e+" ");
			System.out.println();
		}
		else
			System.out.println(-1);
		
		}
	}
}