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.*;
import java.lang.*;
 
import static java.lang.Math.*;
 
public class MakingString implements Runnable 
{
    static class InputReader 
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
 
        public InputReader(InputStream stream) 
        {
            this.stream = stream;
        }
        
        public int read()
        {
            if (numChars==-1) 
                throw new InputMismatchException();
            
            if (curChar >= numChars) 
            {
                curChar = 0;
                try
                {
                    numChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                
                if(numChars <= 0)               
                    return -1;
            }
            return buf[curChar++];
        }
     
        public String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() 
        {
            int c = read();
            
            while(isSpaceChar(c)) 
                c = read();
            
            int sgn = 1;
        
            if (c == '-') 
            {
                sgn = -1;
                c = read();
            }
            
            int res = 0;
            do
            {
                if(c<'0'||c>'9') 
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c)); 
        
            return res * sgn;
        }
        
        public long nextLong() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            long res = 0;
            
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
                return res * sgn;
        }
        
        public double nextDouble() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') 
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c))
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
    
        public String readString() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = read();
            } 
            while (!isSpaceChar(c));
            
            return res.toString();
        }
     
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
     
        public String next()
        {
            return readString();
        }
        
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
	
	
	// if modulo is required set value accordingly
	public static long[][] matrixMultiply2dL(long t[][],long m[][])
	{
		long res[][]= new long[t.length][m[0].length];
		
		for(int i=0;i<t.length;i++)
		{
			for(int j=0;j<m[0].length;j++)
			{
				res[i][j]=0;
				for(int k=0;k<t[0].length;k++)
				{
					res[i][j]+=t[i][k]+m[k][j];
				}
			}
		}
		
		return res;
	}
	
	static long combination(long n,long r)
	{
		long ans=1;
		for(long i=0;i<r;i++)
		{
			ans=(ans*(n-i))/(i+1);
		}
		return ans;
	}
	static int mat(String a,String b)
	{
	    int count=0;
	    for(int i=0;i<a.length();i++)
	    {
	        if(a.charAt(i)!=b.charAt(i))
	            count++;
	        
	    }
	    
	    return count;
	}
	
	static int accumulate(int arr[], int first, 
                                     int last) 
    { 
        int init = 0; 
        for (int i = first; i< last; i++) { 
            init = init + arr[i]; 
        } 
      
        return init; 
    } 
  
    // Returns true if it is possible to divide  
    // array into two halves of same sum.  
    // This function mainly uses combinationUtil() 
    static Boolean isPossible(int arr[], int n) 
    { 
        // If size of array is not even. 
        if (n % 2 != 0) 
            return false; 
  
        // If sum of array is not even. 
        int sum = accumulate(arr, 0, n); 
        if (sum % 2 != 0) 
            return false; 
  
        // A temporary array to store all  
        // combination one by one int k=n/2; 
        int half[] = new int[n/2]; 
  
        // Print all combination using temporary 
        // array 'half[]' 
        return combinationUtil(arr, half, 0, n - 1, 
                                0, n, sum); 
    } 
  
    /* arr[] ---> Input Array 
    half[] ---> Temporary array to store current  
                combination of size n/2 
    start & end ---> Staring and Ending indexes in arr[] 
    index ---> Current index in half[] */
    static Boolean combinationUtil(int arr[], int half[],  
                                   int start, int end, 
                                   int index, int n, 
                                   int sum) 
    { 
        // Current combination is ready to  
        // be printed, print it 
        if (index == n / 2) { 
            int curr_sum = accumulate(half, 0 , n/2); 
            return (curr_sum + curr_sum == sum); 
        } 
  
        // replace index with all possible elements.  
        // The condition "end-i+1 >= n/2-index" makes 
        // sure that including one element at index  
        // will make a combination with remaining 
        // elements at remaining positions 
        for (int i = start; i <= end && end - i + 1 >=  
                                  n/2 - index; i++) { 
            half[index] = arr[i]; 
            if (combinationUtil(arr, half, i + 1, end,  
                                 index + 1, n, sum)) 
                return true; 
        } 
  
        return false; 
    } 
    public static void main(String args[]) throws Exception 
    {
        new Thread(null, new MakingString(),"MakingString",1<<27).start();
    }
	// **just change the name of class from Main to reuquired**
    public void run()
    {
        InputReader sc = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);
		
	    
	    
	    
	        int n = sc.nextInt();
	        
	        for(int i=0;i<n;i++)
	        {
	            int t=sc.nextInt();
	            
	            int arr[]=new int[t];
	            HashMap <Integer,Integer> map = new HashMap();
	            int max=0;
	            int sum=0;
	            for(int j=0;j<t;j++)
	                {
	                    
	                    arr[j]=sc.nextInt();
	                    sum=sum+arr[j];
	                    max=Math.max(arr[j],max);
	                    map.put(arr[j],j);
	                }
	            int res[]=new int[2*t];
	            for(int j=0;j<t;j++)
	            {
	                int temp=arr[j];
	                while(map.containsKey(temp))
	                    {
	                        temp++;
	                    }
	                map.put(temp,1);
	                res[2*j]=arr[j];
	                res[2*j+1]=temp;
	                sum=sum+temp;
	                max=Math.max(temp,max);
	            }
	            max=(max*(max+1))/2;
	            if(max==sum)
	            {
	            for(int j=0;j<2*t;j++)
	            {
	                w.print(res[j] + " ");
	            }
	                
	            }
	            else
	                w.print(-1);
	                
	            w.println("");
	                
	        }
	        
	        
	        
	        
	        
	    
        
    
	    
	    
        System.out.flush();
        w.close();
        
    }
}