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 
/******************************************************************************

                            Online Java Compiler.
                Code, Compile, Run and Debug java program online.
Write your code in this editor and press "Run" button to execute it.

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

public class Main
{
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		
		int t = s.nextInt();
		while(t--!=0) {
		    int n = s.nextInt();
		    if(n < 4) {
		        pw.println(-1);
		        continue;
		    }
		    if(n%2 == 0) {
		        for(int i=2;i<=n;i = i+2) {
		            pw.print(i + " ");
		        }
		        
		        pw.print((n-3) + " " + (n-1) + " ");
		        for(int i=n-5;i>=1;i=i-2){
		            pw.print(i + " ");
		        }pw.println();
		    }
		    else if(n%2 != 0) {
		        for(int i=1;i<=n;i = i+2) {
		            pw.print(i + " ");
		        }
		        
		        pw.print((n-3) + " " + (n-1) + " ");
		        for(int i=n-5;i>1;i=i-2){
		            pw.print(i + " ");
		        }pw.println();
		    }
		    
		}
		pw.flush();
	}
}
