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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class RestoringPermutation1315C {

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		
		int t = sc.nextInt();
		while(t-->0) {
			int n = sc.nextInt();
			int b[] = new int[n];
			TreeSet<Integer> ts = new TreeSet<Integer>();
			for (int i = 1; i <= 2*n; i++)
				ts.add(i);
			
			for (int i = 0; i < n; i++) {				
				b[i] = sc.nextInt();
				ts.remove(b[i]);
			}
			
			int ans[] = new int[2*n];
			boolean imp = false;
			for (int i = 0; i < n && !imp; i++) {
				ans[(2*(i+1) - 1) - 1] = b[i];
				Integer other = ts.higher(b[i]);
				if (other == null)
					imp  = true;
				else {					
					ans[2*(i+1) - 1] = other;
					ts.remove(other);
				}
			}
			
			if (imp) 
				out.print(-1);
			else 				
				for (int i = 0; i < 2*n; i++) {
					if (i > 0)
						out.print(" ");
					out.print(ans[i]);
				}
			
			out.println();
		}
		
		out.flush();
		out.close();
	}
	
	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		public Scanner(FileReader f) {
			br = new BufferedReader(f);
		}

		public Scanner(InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public boolean Ready() throws IOException {
			return br.ready();
		}

		public void waitForInput(long time) {
			long ct = System.currentTimeMillis();
			while (System.currentTimeMillis() - ct < time) {
			}
			;
		}
	}
}