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:
public class p1315C {
    public static void main(String[] args) {
        var sc = new java.util.Scanner(System.in);
        l: for(int t=sc.nextInt();t-->0;) {
            var sb= new StringBuilder();
            int n=sc.nextInt(), j, a[]=new int[n],idx[]=new int[2*n+1];
            for(int i=0;i<n;i++) {
             a[i]=sc.nextInt();
             idx[a[i]]++;
            }
            for(int i:a) {
                j=i;
                while(idx[j]!=0) 
                    if(j+1<idx.length) j++;
                    else {System.out.println("-1"); continue l;}
                idx[j]=1;
                sb.append(i+" "+j+" ");
            }
            System.out.println(sb);
        }
    }
}