A permutation of length n is an array p=[p_1,p_2,...,p_n], which contains every integer from 1 to n (inclusive) and, moreover, each number appears exactly once. For example, p=[3,1,4,2,5] is a permutation of length 5.

For a given number n (n ≥ 2), find a permutation p in which absolute difference (that is, the absolute value of difference) of any two neighboring (adjacent) elements is between 2 and 4, inclusive. Formally, find such permutation p that 2 ≤ |p_i - p_{i+1}| ≤ 4 for each i (1 ≤ i < n).

Print any such permutation for the given integer n or determine that it does not exist.

Input

The first line contains an integer t (1 ≤ t ≤ 100) — the number of test cases in the input. Then t test cases follow.

Each test case is described by a single line containing an integer n (2 ≤ n ≤ 1000).

Output

Print t lines. Print a permutation that meets the given requirements. If there are several such permutations, then print any of them. If no such permutation exists, print -1.

Example

Input


6
10
2
4
6
7
13


Output


9 6 10 8 4 7 3 1 5 2 
-1
3 1 4 2 
5 3 6 2 4 1 
5 1 3 6 2 4 7 
13 9 7 11 8 4 1 3 5 2 6 10 12 
import java.io.*;
import java.util.*;
import java.lang.*;

public class Rextester{
    public static void main(String[] args)throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        StringBuffer sb = new StringBuffer();
        while(t-->0){
            int n = Integer.parseInt(br.readLine());
            if(n<=3){
                sb.append("-1\n");
                continue;
            }
            LinkedList<Integer> answer = new LinkedList<Integer>();
            answer.add(3);
            answer.add(1);
            answer.add(4);
            answer.add(2);
            int count = 5;
            for(int i=count;i<=n;i++){
                if(i%2==0){
                    answer.addFirst(i);
                }
                else{
                    answer.addLast(i);
                }
            }
            for(int i=0;i<answer.size();i++){
                sb.append(answer.get(i)).append(" ");
            }
            sb.append("\n");
        }
        br.close();
        System.out.println(sb);
    }
}
            
                    