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.PrintWriter;
import java.util.*;
 
/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		FastReader s = new FastReader();
		PrintWriter pw = new PrintWriter(System.out);
        int t=s.nextInt();
        while(t-->0){
            int n=s.nextInt();
            if(n>=4){
                int[] arr=new int[n];
                int k=1;
                for(int i=n/2;i<n;i++){
                arr[i]=k;k+=2;
                }
                arr[(n/2)-2]=2;
                arr[(n/2)-1]=4;
                k=6;
                for(int i=((n/2)-3);i>=0;i--){
                    arr[i]=k;k+=2;
                }
                for(int i=0;i<n;i++){
                    System.out.print(arr[i]+" ");
                }
                System.out.println(" ");
            }
            else{
                System.out.println(-1);
            }
        }    
	}
}
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;
	}
}
