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.*;
import java.math.*;

public class HelloWorld {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int t = scanner.nextInt();
        while(t-- > 0) {
            int n = scanner.nextInt();
            int[] arr = new int[n];
            boolean[] a = new boolean[2 * n + 1];
            for(int i =0 ; i < n; i++) {
                arr[i] = scanner.nextInt();
                a[arr[i]] = true;
            }
            int[] result = new int[2 * n];
            boolean works = true;
            for(int i = 0; i < arr.length; i++) {
                int current = arr[i];
                result[i * 2] = current;
                while(current < a.length && a[current++]) {
                    continue;
                }
                current--;
                if(a[current]) {
                    System.out.println(-1);
                    works = false;
                    break;
                }
                a[current] = true;
                result[i * 2 + 1] = current;
            }
            if(!works) {
                continue;
            }
            for(int i = 0; i < result.length; i++) {
                System.out.print(result[i] + " ");
            }
            System.out.println();
        }
    }
}