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.Arrays;
import java.util.Scanner;

public class C_623 {
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        int q = in.nextInt();
        for(int tc=0;tc<q;tc++){
            int n=in.nextInt();
            int[] b = new int[n];
            int[] a = new int[2*n];
            int[] p = new int[2*n+1];
            Arrays.fill(p, 1);
            for(int i=0;i<n;i++){
                b[i] = in.nextInt();
                a[2*i] = b[i];
                p[b[i]] = 0;
            }
            for(int i=0;i<n;i++){
                int j=0;
                for(j=a[2*i]+1;j<=2*n;j++){
                    if(p[j]==1){
                        break;
                    }
                }
                if(j==2*n+1){
                    a[0] = -1;
                    break;
                }
                a[2*i+1] = j;
                p[j] = 0;
            }
            if(a[0]==-1){
                System.out.println(-1);
            }
            else {
                for (int i=0;i<2*n;i++){
                    System.out.print(a[i] + " ");
                }
                System.out.println();
            }
        }
    }
}