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.Scanner;

public class G {
	//  5 2 4 1 3 
	// 6 3 5 1 4 2
	// 7 4 1 5 3 6 2 
	// 8 6 3 1 5 7 4 2
	// 9 6 8 4 7 3 1 5 2 0
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner in = new Scanner(System.in);
		int t= in.nextInt();
		for(int q=0;q<t;q++) {
			int n=in.nextInt();
			if(n<=3) {
				System.out.println("-1");
			}else if(n==4) {
				System.out.println("3 1 4 2");
			}
			else {
				StringBuilder sb =new StringBuilder();
				int count=0;
				 if (n%5==1) {
					 sb.append(n+" ");
						sb.append(n-3+" ");sb.append(n-1+" ");sb.append(n-5+" ");sb.append(n-2+" ");sb.append(n-4+" ");
						n=n-6;
				}else if (n%5==2) {
					 sb.append(n+" ");
						sb.append(n-3+" ");sb.append(n-6+" ");sb.append(n-2+" ");sb.append(n-4+" ");sb.append(n-1+" ");sb.append(n-5+" ");
						n=n-7;	
				}
				else if (n%5==3) {
					 sb.append(n+" ");
						sb.append(n-2+" ");sb.append(n-5+" ");sb.append(n-7+" ");sb.append(n-3+" ");sb.append(n-1+" ");sb.append(n-4+" ");sb.append(n-6+" ");
						n=n-8;	
				}else if (n%5==4) {
					 sb.append(n+" ");
						sb.append(n-3+" ");sb.append(n-1+" ");sb.append(n-5+" ");sb.append(n-2+" ");sb.append(n-6+" ");sb.append(n-8+" ");sb.append(n-4+" ");sb.append(n-7+" ");
						n=n-9;	
				}
				 while(0<n) {
					sb.append(n+" ");
					sb.append(n-3+" ");sb.append(n-1+" ");sb.append(n-4+" ");sb.append(n-2+" ");
					count=+5;
					n=n-5;
				}
				 System.out.println(sb.toString());
			}
		}
	}

}
