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 
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
    static FastReader sc = new FastReader();
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		
		
		int t = sc.nextInt() ;
		
		while(t>0) {
		    int n=sc.nextInt();
		    if(n<=3)
		    {
		        System.out.print("-1");
		    }
		    else if(n%2==0)
		    {
		        for(int i=2;i<=n;i=i+2)
		        {
		            System.out.print(i+" ");
		        }
		        int a1=n-3;
		        int a2=n-1;
		        System.out.print(a1+" "+a2+" ");
		       
		            for(int i=n-5;i>0;i=i-2)
		            {
		                System.out.print(i+" ");
		            }
		    }
		    else{
		         for(int i=1;i<=n;i=i+2)
		        {
		            System.out.print(i+" ");
		        }
		        int a1=n-3;
		        int a2=n-1;
		        System.out.print(a1+" "+a2+" ");
		       
		            for(int i=n-5;i>0;i=i-2)
		            {
		                System.out.print(i+" ");
		            }
		    }
		    System.out.println();
			t--;
		}
	}
	
	
	
	//	FAST I/O
	static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        
        public FastReader()
        {
            br = new BufferedReader(
                new InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt() { return Integer.parseInt(next()); }
 
        long nextLong() { return Long.parseLong(next()); }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
	}
	
	
}










