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.Arrays;
import java.util.Scanner;


public class Watermelon {

	public static void main(String[] args) {

		
		Scanner scanner=new Scanner(System.in);
		int t=scanner.nextInt();
		for(int i=1;i<=t;i++) {
			int n=scanner.nextInt();
			
			System.out.println(specialPermutation(n));
		}
		
		
		

	}
	
	public static int[]shift(int[]arr,int plus){
		for(int i=0;i<arr.length;i++)arr[i]+=plus;
		return arr;
	}

	public static String stringToArr(int[]arr) {
		String s="";
		for(int i=0;i<arr.length;i++)s+=arr[i]+" ";
		return s;
	}
	
	public static String permute(int prefix,int length){
		int[]arr= {};
		int[]four= {2,4,1,3};
		int[]five= {3,1,4,2,5};
		int[]six= {3,5,1,4,2,6};
		int[]seven= {4,1,5,2,6,3,7};
		int[]eight= {2,4,1,3,6,8,5,7};
		int[]nine= {3,1,4,2,5,7,9,6,8};
		int[]ten= {3,1,4,2,5,8,6,9,7,10};
		switch(length) {
		case 4:{
			arr=four;break;}
		case 5:{
			arr=five;break;}
		case 6:{
			arr=six;break;}
		case 7:{
			arr=seven;break;}
		case 8:{
			arr=eight;break;}
		case 9:{
			arr=nine;break;}
		case 10:{
			arr=ten;}
		}
		arr=shift(arr,prefix);
		
		return stringToArr(arr);
	}
	public static String specialPermutation(int n){
		String s="-1";
		if(n>3) {
			s="";
			int pre=0;
			while(n>=11) {
				n-=7;
				s+=permute(pre,7);
				pre+=7;
			}
			s+=permute(pre,n);
		}
		return s;
	}
}
