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.*;

public class CodeForce {
 static ArrayList<Integer> inputarrlist(String[] str){
     ArrayList<Integer> arr=new ArrayList<>();
     for(int i=0;i<str.length;i++)
         arr.add(Integer.parseInt(str[i]));
     
     return arr;
 }
 static int[] inputarr(String[] str){
     int[] arr=new int[str.length];
     for(int i=0;i<str.length;i++)
         arr[i]=(Integer.parseInt(str[i]));
     
     return arr;
 }
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
      int t=Integer.parseInt(br.readLine());
      while(t-->0){
          int n=Integer.parseInt(br.readLine());
          if(n==2 || n==3)
              System.out.println(-1);
          else{
        int temp=n;
        if(n%2==0)
              temp--;
        
        for(int i=temp;i>=1;i=i-2){
              System.out.print(i+" ");
              
        }
          System.out.print(4+" "+2+" ");
          for(int i=6;i<=n;i=i+2)
              System.out.print(i+" ");
          System.out.println("");
      }
      }
}}