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.*;
import java.util.*;
import java.math.*;

public class C {

	public void realMain() throws Exception {

		BufferedReader fin = new BufferedReader(new InputStreamReader(System.in), 1000000);

		String in = fin.readLine();

		String[] ar = in.split(" ");

		int T = Integer.parseInt(ar[0]);
	for(int t = 0; t < T; t++) {
		in = fin.readLine();
		int n = Integer.parseInt(in);

		in = fin.readLine();

		int[] b = new int[n];

		ar = in.split(" ");

		for(int i = 0; i < n; i++) {
			b[i] = Integer.parseInt(ar[i]);
		}

		int[] a = new int[2 * n];

		boolean[] used = new boolean[2*n + 1];

		for(int i = 0; i < n; i++) {
			a[2*i] = b[i];
			used[b[i]] = true;
		}

		for(int i = 1; i < 2*n; i+=2) {
			int min = a[i - 1] + 1;
			for(int j = 0; j + min <= 2*n; j++) {
				if( !used[j + min] ) {
					a[i] = j + min;
					used[j + min] = true;
					break;
				}
			}
		}

		boolean[] newused = new boolean[2*n + 1];

		for(int i = 0; i < 2*n; i++) {
			newused[a[i]] = true;
		}

		boolean win = true;
		for(int i = 1; i < 2*n + 1; i++) {
			if(!newused[i]) {
				win = false;
			}
		}

		if(!win) {
			System.out.println(-1);
		} else {
			for(int i = 0; i < 2*n; i++) {
				System.out.print(a[i] + " ");
			}
			System.out.println();
		}
		
	}


	}


	public static void main(String[] args) throws Exception {
		C c = new C();
		c.realMain();
	}
}