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.*;
public class Problem1315c {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t-- > 0) {
            int n = sc.nextInt();
            int[] getLine = new int[n];
            int[] numLine = new int[210];
            for (int j = 0; j < n; j++) {
                int b = sc.nextInt();
                numLine[b]++;
                getLine[j] = b;
            }
            boolean noperm = true;
            int numHave = 0;
            for (int j = 1; j < n * 2; j++) {
                if (numLine[j] > 1) {
                    noperm = false;
                    break;
                }
                if (numLine[j] == 1) {
                    numHave++;
                }
                if (j % 2 == 1) {
                    if (numHave < j / 2 + 1) {
                        noperm = false;
                        break;
                    }
                }
            }
            if (!noperm) {
                System.out.println("-1");
                continue;
            }
            for (int j = 0; j < n; j++) {
                System.out.print(getLine[j] + " ");
                for (int k = getLine[j] + 1; ; k++) {
                    if (numLine[k] == 0) {
                        System.out.print(k + " ");
                        numLine[k] = 1;
                        break;
                    }
                }
            }
            System.out.println();
        }
        System.out.flush();
    }
}