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.Scanner;

public class R623_C {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        for (int r = 0; r < t; r++) {
            int n = in.nextInt();
            int[] b = new int[n + 1];
            int[] a = new int[2*n + 1];
            for (int i = 1; i < n + 1; i++) {
                int num = in.nextInt();
                b[i] = num;
                a[num] = 1;
            }
            
            int[] res = new int[2*n + 1];
            int ans = 0;
            for (int i = 1; i < n + 1; i++) {
                   res[2*i - 1] = b[i];
                   int num = b[i] + 1;
                   while (num <= 2*n) {
                        if (a[num] != 1) {
                            res[2*i] = num;
                            a[num]++;
                            break;
                        }
                        num++;
                    }
                    if (num == 2*n + 1) {
                        ans = -1;
                        break;
                    }
            }
            if (ans == -1) {
                System.out.print(-1);
            } else {
                for (int i = 1; i < 2 * n + 1; i++)
                    System.out.print(res[i] + " ");
            }
            System.out.println();
        }
        in.close();
    }
}