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.Arrays;

public class C {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        StringBuilder sb = new StringBuilder();
        int t = Integer.parseInt(br.readLine());
        for (int i = 0; i < t; i++) {
            int n = Integer.parseInt(br.readLine());
            boolean[] check = new boolean[n * 2 + 1];
            String[] strArr = br.readLine().split(" ");
            int[] bArr = new int[n];
            for (int j = 0; j < n; j++) {
                bArr[j] = Integer.parseInt(strArr[j]);
                check[bArr[j]] = true;
            }
            boolean isPossible = true;

            int[] aArr = new int[2 * n];
            for (int j = 0; j < n; j++) {
                aArr[j * 2] = bArr[j];
                int tmp = aArr[j * 2];
                do{
                    tmp++;
                    if(tmp > n * 2){
                        isPossible = false;
                        break;
                    }
                } while(check[tmp]);
                if(tmp > n * 2){
                    isPossible = false;
                    break;
                }
                aArr[j * 2 + 1] = tmp;
                check[tmp] = true;
            }

            if(isPossible){
                for (int j = 0; j < n * 2; j++) {
                    sb.append(aArr[j]).append(" ");
                }
            }else{
                sb.append(-1);
            }
            sb.append("\n");
        }
        bw.write(sb.toString());
        bw.flush();
        bw.close();
        br.close();
    }
}