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.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Hashtable;
import java.util.StringTokenizer;

public class Solution {
	public static void main ( String args [] ) throws IOException, InterruptedException {
	
	
			solve();}

	   
public static void solve() throws IOException, InterruptedException {
Scanner sc = new Scanner(System.in);
int x= sc.nextInt();
all:for(int c=0;c<x;c++) {
int n=sc.nextInt();
int keep=n;
int arr[] = new int[n];
if(n<=3) {
	System.out.println(-1);
	continue all;
}
int j=0;
for(int i=2;i<=n;i+=2) {
	arr[j]=i;
	j++;
}
if(n%2==0) {
	n--;
}
for(int i=n;i>0;i-=2) {
	arr[j]=i;
	j++;
}
if(keep%2==0) {

for(int i=0;i<arr.length-1;i++) {
	if(arr[i]%2!=0) {
		int temp = arr[i+1];
		arr[i+1]=arr[i];
		arr[i]=temp;
		break;
	}
}
for(int i=0;i<arr.length;i++) {
	System.out.print(arr[i]+" ");
}
System.out.println();
}else {
	for(int i=0;i<arr.length-1;i++) {
		if(arr[i]%2!=0) {
			int temp = arr[i+2];
			arr[i+2]=arr[i];
			arr[i]=temp;
			temp = arr[i+2];
			arr[i+2]=arr[i+1];
			arr[i+1]=temp;
			break;
		}
	}
	for(int i=0;i<arr.length;i++) {
		System.out.print(arr[i]+" ");
	}
	System.out.println();
}


}
}









	
	
	
	
	
	



















static void shuffle(int[] a)
{
	int n = a.length;
	for(int i = 0; i < n; i++)
	{
		int r = i + (int)(Math.random() * (n - i));
		int tmp = a[i];
		a[i] = a[r];
		a[r] = tmp;
	}
}




}

@SuppressWarnings("rawtypes")
class Pair implements Comparable{
	int x;
	int y;

	@Override
	public int hashCode() {
		final int prime = 31;
		int result = 1;
		result = prime * result + x;
		result = prime * result + y;
		return result;
	}

	@Override
	public boolean equals(Object obj) {
		if (this == obj)
			return true;
		if (obj == null)
			return false;
		if (getClass() != obj.getClass())
			return false;
		Pair other = (Pair) obj;
		if (x != other.x)
			return false;
		if (y != other.y)
			return false;
		return true;
	}

	public Pair(int x , int y) {
		this.x=x;
		this.y=y;
	}

	@Override
	public int compareTo(Object o) {
		Pair p = (Pair)o;
		if(this.x<p.x) return -1;
		if(this.y>p.y) return 1;
		return 0;
	}


}




class Scanner 
{
	StringTokenizer st;
	BufferedReader br;

	public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

	public String next() throws IOException 
	{
		while (st == null || !st.hasMoreTokens()) 
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}

	public int nextInt() throws IOException {return Integer.parseInt(next());}
	
	public long nextLong() throws IOException {return Long.parseLong(next());}

	public String nextLine() throws IOException {return br.readLine();}
	
	public double nextDouble() throws IOException
	{
		String x = next();
		StringBuilder sb = new StringBuilder("0");
		double res = 0, f = 1;
		boolean dec = false, neg = false;
		int start = 0;
		if(x.charAt(0) == '-')
		{
			neg = true;
			start++;
		}
		for(int i = start; i < x.length(); i++)
			if(x.charAt(i) == '.')
			{
				res = Long.parseLong(sb.toString());
				sb = new StringBuilder("0");
				dec = true;
			}
			else
			{
				sb.append(x.charAt(i));
				if(dec)
					f *= 10;
			}
		res += Long.parseLong(sb.toString()) / f;
		return res * (neg?-1:1);
	}
	
	public boolean ready() throws IOException {return br.ready();}


}