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.*;
public class code {
	static PrintWriter pw;
	static boolean[] visit;
	static ArrayList<Pair>[] adj;
	static ArrayList<Integer> list;
	static long max=01;
	static void dfs(int i, long c) {
		visit[i]=true;
		max=Math.max(c, max);
		for(Pair p: adj[i]) {
			if(!visit[p.x-1]) {
				dfs(p.x-1, c+1l*p.y);
			}
		}
	}
	public static double dist(Pair a, Pair b) {
		return Math.sqrt((a.x-b.x)*(a.x-b.x)+ (a.y-b.y)*(a.y-b.y));
	}
	static int large(int x, int[] arr) {
		int ans=-1;
		int start=0,end=arr.length-1;
		while(start<=end) {
			int mid=(start+end)/2;
			if(arr[mid]<=x) {
				start=mid+1;
			}else {
				ans=mid;
				end=mid-1;
			}
		}
		return ans;
	}
	static boolean pf(int n) {
		return Math.abs(Math.sqrt(n)*Math.sqrt(n)-n)<=1e-8;
	}
	static boolean sign(int n) {
		return n>0;
	}
	public static void main(String[] args) throws Exception {
		Scanner sc= new Scanner(System.in);
		pw = new PrintWriter(System.out);
		int t=sc.nextInt();
		while(t-->0) {
			int n=sc.nextInt();
			int[] arr=new int[n];
			HashSet<Integer> taken=new HashSet<Integer>();
			for(int i=0; i<n; i++) {
				arr[i]=sc.nextInt();
				taken.add(arr[i]);
			}
			int[] arr2=new int[n];
			int j=0;
			for(int i=1; i<=2*n; i++) {
				if(!taken.contains(i)) {
					arr2[j]=i;
					j++;
				}
			}
			boolean valid=true;
			ArrayList<Integer> list=new ArrayList<Integer>();
			for(int i=0; i<n-1; i++) {
				int idx=large(arr[i],arr2);
				if(idx==-1) {
					valid=false;
					break;
				}else {
					list.add(arr[i]);
					list.add(arr2[idx]);
					arr2[idx]=0;
					Arrays.sort(arr2);
				}
			}
			int idx=large(arr[n-1],arr2);
			if(idx==-1) {
				valid=false;
			}else {
				list.add(arr[n-1]);
				list.add(arr2[idx]);
			}
			if(!valid) {
				pw.println(-1);
			}else {
				for(int i=0; i<2*n-1; i++) {
					pw.print(list.get(i)+" ");
				}
				pw.println(list.get(2*n-1));
			}
		}
		
		pw.close();
	}
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;
 
		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}
 
		public Scanner(FileReader r) {
			br = new BufferedReader(r);
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public int[] nextArr(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < arr.length; i++)
				arr[i] = nextInt();
			return arr;
		}
		public Integer[] nextsort(int n) throws IOException{
			Integer[] arr=new Integer[n];
			for(int i=0; i<n; i++) 
				arr[i]=nextInt();
			return arr;
		}
		public boolean ready() throws IOException {
			return br.ready();
		}
	}
	static class Pair implements Comparable<Pair>{
		int x;
		int y;
		public Pair(int a, int b) {
			this.x=a;
			this.y=b;
		}
		public int compareTo(Pair other) {
			return this.y-other.y;
		}
	}
	static class Triple implements Comparable<Triple>{
		int x;
		int y;
		boolean d;
		public Triple(int a, int b, boolean t) {
			this.x=a;
			this.y=b;
			this.d=t;
		}
		public int compareTo(Triple other) {
			if(this.d && !other.d) {
				return 1;
			}else if(!this.d && other.d) {
				return -1;
			}else {
				return this.y-other.y;
			}
		}
	}
}