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 Task{
// taking inputs
static BufferedReader s;
static BufferedWriter out;
static String read() throws IOException{String line="";while(line.length()==0){line=s.readLine();continue;}return line;}
static int int_v (String s1){return Integer.parseInt(s1);}
static long long_v(String s1){return Long.parseLong(s1);}
static int[] int_arr() throws IOException{String[] a=read().split(" ");int[] b=new int[a.length];for(int i=0;i<a.length;i++){b[i]=int_v(a[i]);}return b;}
static long[] long_arr() throws IOException{String[] a=read().split(" ");long[] b=new long[a.length];for(int i=0;i<a.length;i++){b[i]=long_v(a[i]);}return b;}
static void assign(){s=new BufferedReader(new InputStreamReader(System.in));out=new BufferedWriter(new OutputStreamWriter(System.out));}
// ends

//......................................@uthor_Alx..............................................

public static void main(String[] args) throws  IOException{
	        assign(); 
          	int t=int_v(read()),c=1;
          	while(t--!=0){
          		int n=int_v(read());
          		int[] a1=int_arr();
          		boolean b1=true;
          		boolean[] b=new boolean[2*n+1];
          		int[][] res=new int[n][2];
          		for(int i=0;i<n;i++){res[i][0]=a1[i];}
          		for(int x:a1){b[x]=true;}
          		for(int i=0;i<n;i++){
          			boolean bb=false;
          			for( int j=1;j<=2*n;j++){
          				if(!b[j]&&j>a1[i]){
          					bb=true;res[i][1]=j; b[j]=true;break;
          				}
          			}
          			if(!bb){out.write("-1\n");b1=false;break;}
          		}
          		if(!b1){continue;}
          		for(int i=0;i<n;i++){
          			out.write(res[i][0]+" "+res[i][1]+" ");
          		}
          		out.write("\n");
          		
          	}
       out.flush();
   }
}