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.util.*;
import java.io.*;

public class Main {
    static StringBuilder sb = new StringBuilder();
    static BufferedReader br = null;
    static StringTokenizer st = null;
    static int n;
    static int[] ba;
    static boolean[] ck;
    
	public static void main(String[] args) throws Exception {
		br = new BufferedReader(new InputStreamReader(System.in));
		st = null;
		int tc = Integer.parseInt(br.readLine());
		while(tc-- >0) {
			n = Integer.parseInt(br.readLine());
			st = new StringTokenizer(br.readLine());
			ba = new int[n+1];
			ck = new boolean[2*n+2];
			boolean flg = false;
			for(int i=1; i<=n; i++) {
				ba[i] = Integer.parseInt(st.nextToken());
				if(ba[i]>=2 * n) {
					flg = true;
				}else {
					ck[ba[i]]=true;
				}
			}
			StringBuilder ans = new StringBuilder();
			for(int i=1; i<=n; i++) {
				ans.append(ba[i]).append(" ");
				int tmp = ++ba[i];
				while(ck[tmp] && tmp<=2*n) {
					tmp++;
				}
				if(tmp<=2*n) {
					ans.append(tmp).append(" ");
					ck[tmp]=true;	
				}else {
					flg = true;
					break;
				}
			}
			if(flg) sb.append("-1").append("\n");
			else sb.append(ans).append("\n");
		}
		System.out.println(sb);
	}
}