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 static java.lang.Math.*;

import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;

public class A {

	public static void main(String[] args) throws NumberFormatException, IOException {
		// TODO Auto-generated method stub
		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[] a = new int[2 * n];
			int[] b = new int[2 * n];
			for (int i = 0; i < b.length; i += 2) {
				a[i] = Integer.parseInt(st.nextToken());
				b[a[i] - 1] = 1;
			}
			boolean f = true;
			for (int i = 0; i < b.length; i += 2) {
				int idx = -1;
				for (int j = a[i]; j < 2*n; j++) {
					if (b[j] == 0) {
						idx = j + 1;
						b[j] = 1;
						break;
					}
				}
				if (idx == -1) {
					f = false;
					break;
				}
				a[i + 1] = idx;
			}
			if (!f)
				pw.println(-1);
			else {
				for (int i = 0; i < b.length; i++) {
					pw.print(a[i] + " ");
				}
				pw.println();
			}

		}
		pw.flush();
		pw.close();

	}

	
}