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:
// @uthor -: puneet
// TimeStamp -: 23/02/20 

import java.io.*;
import java.util.*;

public class R622Q1 implements Runnable {

    private boolean testCases=true;
    private boolean console=false;
    
    public void solve() {
        int n=in.ni();
        ArrayList<Integer> list=new ArrayList<>();
        TreeSet<Integer> set=new TreeSet<>();
        TreeSet<Integer> tset=new TreeSet<>();
        boolean isok=true;
        int[] arr=new int[n];
        for(int i=0;i<n;++i){
            int num=in.ni();
            arr[i]=num;
            tset.add(arr[i]);
        }

        for(int i=0;i<n;++i){
            int num=arr[i];
            if(set.contains(num)){
                isok=false;
            }else {
                list.add(num);
                set.add(num);
                for(int j=num+1;j<500;++j){
                    if(!set.contains(j) && !tset.contains(j)){
                        set.add(j);
                        list.add(j);
                        break;
                    }
                }
            }

            if(set.last()>2*n){
                isok=false;
            }
        }
        if(!isok){
            out.print("-1");
        }else {
            for(int i:list){
                out.print(i+" ");
            }
        }
        out.println();
    }

    /* -------------------- Templates and Input Classes -------------------------------*/

    @Override
    public void run() {
        try {
            init();
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
        int t= testCases ? in.ni() : 1;
        while (t-->0) {
            solve();
            out.flush();
        }
    }

    private FastInput in;
    private PrintWriter out;
    public static void main(String[] args) throws Exception {
        new R622Q1().run();
//        new Thread(null, new R622Q1(), "Main", 1 << 27).start();
    }
    private void init() throws FileNotFoundException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        try {
            if (!console && System.getProperty("user.name").equals("puneet")) {
                outputStream = new FileOutputStream("/home/puneet/Desktop/output.txt");
                inputStream = new FileInputStream("/home/puneet/Desktop/input.txt");
            }
        } catch (Exception ignored) {
        }
        out = new PrintWriter(outputStream);
        in = new FastInput(inputStream);
    }
    private void sort(int[] arr) {
        List<Integer> list = new ArrayList<>();
        for (int object : arr) list.add(object);
        Collections.sort(list);
        for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
    }
    private void sort(long[] arr) {
        List<Long> list = new ArrayList<>();
        for (long object : arr) list.add(object);
        Collections.sort(list);
        for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
    }
    public long ModPow(long x, long y, long MOD) {
        long res = 1L;
        x = x % MOD;
        while (y >= 1) {
            if ((y & 1) > 0) res = (res * x) % MOD;
            x = (x * x) % MOD;
            y >>= 1;
        }
        return res;
    }
    public int gcd(int a, int b) {
        if (a == 0) return b;
        return gcd(b % a, a);
    }
    public long gcd(long a, long b) {
        if (a == 0) return b;
        return gcd(b % a, a);
    }
    static class FastInput { InputStream obj;
        public FastInput(InputStream obj) {
            this.obj = obj;
        }
        byte inbuffer[] = new byte[1024];
        int lenbuffer = 0, ptrbuffer = 0;
        int readByte() { if (lenbuffer == -1) throw new InputMismatchException();
            if (ptrbuffer >= lenbuffer) { ptrbuffer = 0;
                try { lenbuffer = obj.read(inbuffer);
                } catch (IOException e) { throw new InputMismatchException(); } }
            if (lenbuffer <= 0) return -1;return inbuffer[ptrbuffer++]; }
        String ns() { int b = skip();StringBuilder sb = new StringBuilder();
            while (!(isSpaceChar(b))) // when nextLine, (isSpaceChar(b) && b!=' ')
            { sb.appendCodePoint(b);b = readByte(); }return sb.toString();}
        int ni() {
            int num = 0, b;boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') { minus = true;b = readByte(); }
            while (true) { if (b >= '0' && b <= '9') { num = num * 10 + (b - '0'); } else {
                    return minus ? -num : num; }b = readByte(); }}
        long nl() { long num = 0;int b;boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') { minus = true;b = readByte(); }
            while (true) { if (b >= '0' && b <= '9') { num = num * 10L + (b - '0'); } else {
                    return minus ? -num : num; }b = readByte(); } }
        boolean isSpaceChar(int c) {
            return (!(c >= 33 && c <= 126));
        }
        int skip() { int b;while ((b = readByte()) != -1 && isSpaceChar(b)) ;return b; }
        float nf() {return Float.parseFloat(ns());}
        double nd() {return Double.parseDouble(ns());}
        char nc() {return (char) skip();}
    }

}