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.*;

public class Main
{

    public static void process()throws IOException
    {
        int n=ni(),arr[]=new int[n+1];
        HashSet<Integer> t_set = new HashSet<Integer>();
        for(int i=1;i<=n;i++){
            t_set.add(arr[i]=ni());
        }


        TreeSet<Integer> set = new TreeSet<Integer>();
       // StringBuilder res = new StringBuilder();

        for(int i=1;i<=2*n;i++){
            if(!t_set.contains(i))
                set.add(i);
        }
        ArrayList<Integer> li = new ArrayList<>();
        li.add(0);
        for(int i=1;i<=n;i++){
            Integer x=set.higher(arr[i]);
            if(x==null){
                pn(-1);
                return;
            }

            li.add(arr[i]);
            li.add(x);
            set.remove(x);
        }
        for(int i=1;i<=2*n;i++) p(li.get(i)+" ");
        pn("");
    }


    static AnotherReader sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        out = new PrintWriter(System.out);
        sc=new AnotherReader();
        boolean oj = true;

        oj = System.getProperty("ONLINE_JUDGE") != null;
        if(!oj) sc=new AnotherReader(100);

        long s = System.currentTimeMillis();
        int t=1;
        t=ni();
        while(t-->0)
            process();
        out.flush();
        if(!oj)
            System.out.println(System.currentTimeMillis()-s+"ms");
        System.out.close();  
    }
    
    
    static void pn(Object o){out.println(o);}
    static void p(Object o){out.print(o);}
    static void pni(Object o){out.println(o);System.out.flush();}
    static int ni()throws IOException{return sc.nextInt();}
    static long nl()throws IOException{return sc.nextLong();}
    static double nd()throws IOException{return sc.nextDouble();}
    static String nln()throws IOException{return sc.nextLine();}
    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}
    static boolean multipleTC=false;
    static long mod=(long)1e9+7l;

    static void r_sort(int arr[],int n){
        Random r = new Random(); 
        for (int i = n-1; i > 0; i--){ 
            int j = r.nextInt(i+1); 
                  
            int temp = arr[i]; 
            arr[i] = arr[j]; 
            arr[j] = temp; 
        } 
        Arrays.sort(arr); 
    }

    static long mpow(long x, long n) {
        if(n == 0)
            return 1;
        if(n % 2 == 0) {
            long root = mpow(x, n / 2);
            return root * root % mod;
        }else {
            return x * mpow(x, n - 1) % mod;
        }
    }
    
    static long mcomb(long a, long b) {
        if(b > a - b)
            return mcomb(a, a - b);
        long m = 1;
        long d = 1;
        long i;
        for(i = 0; i < b; i++) {
            m *= (a - i);
            m %= mod;
            d *= (i + 1);
            d %= mod;
        }
        long ans = m * mpow(d, mod - 2) % mod;
        return ans;
    }
/////////////////////////////////////////////////////////////////////////////////////////////////////////

    static class AnotherReader{BufferedReader br; StringTokenizer st;
    AnotherReader()throws FileNotFoundException{
    br=new BufferedReader(new InputStreamReader(System.in));}
    AnotherReader(int a)throws FileNotFoundException{
    br = new BufferedReader(new FileReader("input.txt"));}
    String next()throws IOException{
    while (st == null || !st.hasMoreElements()) {try{
    st = new StringTokenizer(br.readLine());}
    catch (IOException  e){ e.printStackTrace(); }}
    return st.nextToken(); } int nextInt() throws IOException{
    return Integer.parseInt(next());}
    long nextLong() throws IOException
    {return Long.parseLong(next());}
    double nextDouble()throws IOException { return Double.parseDouble(next()); }
    String nextLine() throws IOException{ String str = ""; try{
    str = br.readLine();} catch (IOException e){
    e.printStackTrace();} return str;}}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
}