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.*;
import java.math.BigInteger;

public class C1315{
    static int gcd(int a, int b) 
    { 
        if (a == 0) 
            return b; 
        if (b == 0) 
            return a; 
        int k; 
        for (k = 0; ((a | b) & 1) == 0; ++k)  
        { 
            a >>= 1; 
            b >>= 1; 
        } 
        while ((a & 1) == 0) 
            a >>= 1; 

        do { 
            while ((b & 1) == 0) 
                b >>= 1; 
            if (a > b)  
            { 
                int temp = a; 
                a = b; 
                b = temp; 
            } 

            b = (b - a); 
        } while (b != 0); 
        return a << k; 
    }   
    static int lcm(int a,int b){
        return a*b/gcd(a,b);
    }
	public static int binary(int arr[],int n, int a,int beg,int end){
		while(beg<=end){
			int mid=beg+(end-beg)/2;
			if(arr[mid]==a)
				return mid;
			if(arr[mid]<a)
				end=mid-1;
			else
				beg=mid+1;
		}
		return -1;
	}
    
    public static int binaryless(int arr[],int n, int a,int beg,int end){
        while(beg<=end){
            int mid=beg+(end-beg)/2;
            if(arr[mid]>=a){
                if(mid==1||arr[mid-1]<a)
                    return mid;
                end=mid-1;
            }
            else{
                beg=mid+1;
            }
        }
        return -1;
    }
	public static void sieve(int t){
		boolean srr[]=new boolean[t+1];
        
        for(int i=2;i*i<=t;i++)
        {
            if(!srr[i])
            {
                for(int k=i*i;k<=t;k+=i)
                    srr[k]=true;
            }
        }
        for(int i=2;i<t+1;i++){
        	if(!srr[i])
            	System.out.println(i);
        }
	}
    static int power(int x, int y, int p) 
    { 
        int res = 1;      
        x = x % p;  
        while (y > 0) 
        { 
            if((y & 1)==1) 
                res = (res * x) % p; 
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res; 
    } 
    
    static class Custom implements Comparable<Custom>{
        int d;
        int f;
        public Custom(int d,int f){
            this.d=d;
            this.f=f;
        }
        public int compareTo(Custom t){
            return this.d-t.d;
        }
    }
    void solve() throws IOException {
        int t=nextInt();
        outer:
        while(t--!=0){
            int n=nextInt();
            int ck[]=new int[n];
            boolean arr[]=new boolean[2*n+1];
            
            for(int i=0;i<n;i++){
                ck[i]=nextInt();
                arr[ck[i]]=true;;   
            }
            int pt=0,upt=0;
            for(int i=2*n;i>0;i--){
                if(arr[i])
                    pt++;
                else upt++;
                if(pt>upt){
                    pw.println(-1);
                    continue outer;
                }
            }
            for(int i:ck){
                pw.print(i+" ");
                for(int j=i+1;j<=2*n;j++){
                    if(!arr[j]){
                        arr[j]=true;
                        pw.print(j+" ");
                        break;
                    }
                }
            }
            pw.println();
            
        }
    }
	String next() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(br.readLine());
        }
        return st.nextToken();
    }
    String nextLine()throws IOException{
        return br.readLine();
    }
    int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    long nextLong() throws IOException {
        return Long.parseLong(next());
    }
 
    StringTokenizer st;
    BufferedReader br;
    PrintWriter pw;
    Scanner sc;
    void run() throws IOException {
        sc=new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(System.out);
        long time = System.currentTimeMillis();
        solve();
        System.err.println("time = " + (System.currentTimeMillis() - time));
        pw.close();
    }
 
    public static void main(String[] args) throws IOException {
        new C1315().run();
    }
 
}