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 
//make sure to make new file!
import java.io.*;
import java.util.*;

public class G640{
   
   public static void main(String[] args)throws IOException{
      BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
      PrintWriter out = new PrintWriter(System.out);
      
      int t = Integer.parseInt(f.readLine());
      
      for(int q = 1; q <= t; q++){
      
         int n = Integer.parseInt(f.readLine());
         
         if(n < 4){
            out.println("-1");
            continue;
         }
         
         ArrayList<Integer> answer = new ArrayList<Integer>();
         if(n%2 == 0){
            //add all evens
            for(int k = 2; k <= n; k+=2){
               answer.add(k);
            }
            answer.add(n-3);
            answer.add(n-1);
            for(int k = n-5 ;k >= 1; k-= 2){
               answer.add(k);
            }
         
         
         } else {
            for(int k = 1; k <= n; k+=2){
               answer.add(k);
            }
            answer.add(n-3);
            answer.add(n-1);
            for(int k = n-5 ;k >= 1; k-= 2){
               answer.add(k);
            }
         
         
         
         }
         
         StringJoiner sj = new StringJoiner(" ");
         for(int i : answer){
            sj.add("" + i);
         }
         
         out.println(sj.toString());
      
      
      }
      
      
      
      
      out.close();
   }
   
      
}