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.util.*;
import java.io.*;
import java.math.BigInteger;

 
public class Main{
  
	static class Node{
		int val;
		Node left, right;
		  public Node(int item) {
			  val = item;
			  left = right = null;
		  }
	}
	
	static class BinaryTree{
		Node root;
		BinaryTree(int val){
			root = new Node(val);
			
		}
	}

	
	static int height(Node root) {
		if(root == null)return 0;
		int left = 1+height(root.left);
		int right = 1+height(root.right);
		
		return Math.max(left,right);
	}
	static int sum = 0;
	static void leavesSum(Node root,int level, int h) {
	  
	  
	    
		if(root.left == null && root.right == null && (level+1) == h) {
			
			  sum += root.val;
		}
		if(root.left != null) {
			leavesSum(root.left,level+1,h);
		}
		if(root.right != null) {
			leavesSum(root.right,level+1,h);
		}
	}
		
	public static void main(String args[])throws IOException{
		

		BufferedReader ob = new BufferedReader(new InputStreamReader(System.in));
	   
       int t = Integer.parseInt(ob.readLine());
       
       while(t --> 0) {
    	   int n = Integer.parseInt(ob.readLine());
    	   
    	   if(n == 2 || n == 3) {
    		   System.out.println(-1);
    	   }else if(n%2 == 0) {
    		   
    		   for(int i = n-1; i >= 1; i-= 2) {
    			   System.out.print(i+" ");
    		   }
    		   System.out.print(4+" "+2+" ");
    		   
    		   for(int i = 6; i <= n; i+=2) {
    			   System.out.print(i+" ");
    		   }
    		   System.out.println();
    	   }else {
    		   for(int i = n; i >= 1; i-= 2) {
    			   System.out.print(i+" ");
    		   }
    		   System.out.print(4+" "+2+" ");
    		   for(int i = 6; i < n; i+=2) {
    			   System.out.print(i+" ");
    		   }
    		   System.out.println();
    	   }
       }
	}
}