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.*;
import java.util.*;
public class RestoringPermutation{
    static Scanner sc = new Scanner(System.in);

    static void restorePermutation(){
        int n = sc.nextInt();
        boolean map[] = new boolean[(2*n + 1)];
        int input[] = new int[n];
        int output[] = new int[n];

        map[0] = true;
        for(int i=0;i<n;i++){
            int index = sc.nextInt();
            input[i] = index;
            map[index] = true;
        }
        for(int i=0;i<n;i++)
        {
            int curr = input[i];
            map[0] = false;
            for(int j=curr+1;j<=2*n;j++)
            {
                if(!map[j])
                {
                    output[i] = j;
                    map[j] = true;
                    map[0] = true;
                    break;
                }
            }
            if(!map[0])
                break;

        }
        if(map[0])
        {
            for(int i=0;i<n;i++)
                System.out.print(input[i] + " " + output[i] + " ");
        }
        else
            System.out.print(-1);
        System.out.println();
    }
    public static void main(String[] args) {
        int t = sc.nextInt();
        while(t--  > 0)
            restorePermutation();
    }
}