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.io.*;
import java.util.ArrayList;
import java.util.List;

public class Solution {
    public static void main(String[] args) throws IOException {
        StreamTokenizer in = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
        PrintWriter out = new PrintWriter(System.out);
        int testNum = nextInt(in);
        int numCount;
        int[] resArray;
        for (int i = 0; i < testNum; i++) {
            numCount = nextInt(in);
            resArray = new int[numCount * 2];
            List<Integer> usedNums= new ArrayList<>();
            for (int j = 0; j < numCount; j++) {
                resArray[(j + 1) * 2 - 2] = nextInt(in);
                usedNums.add(resArray[(j + 1) * 2 - 2]);
            }
            solve(numCount, resArray, usedNums);
        }
    }

    private static void solve(int numCount, int[] resArray, List<Integer> usedNums) {
        int tmpNum;
        for (int j = 1; j < numCount * 2; j += 2) {
            tmpNum = resArray[j - 1] + 1;
            while (usedNums.contains(tmpNum)) {
                tmpNum++;
            }
            if (tmpNum > numCount * 2) {
                System.out.println(-1);
                return;
            } else {
                usedNums.add(tmpNum);
                resArray[j] = tmpNum;
            }
        }
        for (int i = 0; i < numCount * 2; i++) {
            System.out.print(resArray[i] + " ");
        }
        System.out.println();
    }

    private static int nextInt(StreamTokenizer in) throws IOException {
        in.nextToken();
        return (int) in.nval;
    }

}