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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Random;
import java.util.StringTokenizer;



public class A
{
	static class Pair
	{
	    int a;
	    int b;
	    Pair(int a,int b)
	    {
	        this.a = a;
	        this.b = b;
	    }
	    public int hashCode(){
	        //System.out.println("In hashcode");
	        int hashcode = 0;
	        hashcode = a*20;
	        hashcode += b*20;
	        return hashcode;
	    }
	     
	    public boolean equals(Object obj){
	        //System.out.println("In equals");
	        if (obj instanceof Pair) {
	            Pair pp = (Pair) obj;
	            return (pp.a == this.a && pp.b == this.b);
	        } else {
	            return false;
	        }
	    
	}
	}
    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;
        }
    }

    static int gcd(int a,int b)
	{
		if(a == 0) return b;
		if(b == 0) return a;
		
		return gcd(b,a%b);
	}
    
    
    
    public static void main(String[] args)
    {
        OutputStream outputStream = System.out;
        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(outputStream);
        
        int t = sc.nextInt();
        while(t-- > 0)
        {
        	int n = sc.nextInt();
        	
        	if(n == 2 || n == 3)
        	{
        		out.println(-1);
        	}
        	else
        	{	
        		Deque<Integer> dq = new LinkedList<Integer>();
        		dq.addLast(3);
        		dq.addLast(1);
        		dq.addLast(4);
        		dq.addLast(2);
        		
        		int cnt = n-4;
        		int v = 5;
        		int f = 0;
        		while(cnt-- > 0)
        		{
        			if(f == 1)
        			{
        				dq.addFirst(v);
        				v++;
        				f = 0;
        			}
        			else
        			{
        				dq.addLast(v);
        				v++;
        				f = 1;
        			}
        		}
        		
        		for(int i:dq)
        		{
        			out.print(i+" ");
        		}
        		out.println();
        	}
        }
        
        out.close();
    }

}