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 hmm {
	public static void main(String[] args) {
		Scanner scan=new Scanner(System.in);
		int[] sol4={2,4,1,3}, sol6={1,5,3,6,4,2};
		int t=scan.nextInt();
		for(int tt=0;tt<t;tt++) {
			int n=scan.nextInt();
			if(n<=3) {
				System.out.println(-1);
				continue;
			}
			int[] res=new int[n];
			if(n%2==0) {
				int id=0;
				while(id<n) {
					if(id+6==n) {
						for(int j=id;j<id+6;j++) res[j]=sol6[j-id]+id;
						id+=6;
					}
					else {
						for(int j=id;j<id+4;j++) res[j]=sol4[j-id]+id;
						id+=4;
					}
				}
			}
			else {
				if(n==5) {
					System.out.println("1 3 5 2 4");
					continue;
				}
				else if(n==7) {
					System.out.println("5 1 3 6 2 4 7");
					continue;
				}
				else {
					//subtract 5 and do even for the rest
					res[0]=1;
					res[1]=3;
					res[2]=5;
					res[3]=2;
					res[4]=4;
					int id=5;
					while(id<n) {
						if(id+6==n) {
							for(int j=id;j<id+6;j++) res[j]=sol6[j-id]+id;
							id+=6;
						}
						else {
							for(int j=id;j<id+4;j++) res[j]=sol4[j-id]+id;
							id+=4;
						}
					}
				}
			}
			for(int i:res) System.out.print(i+" ");
			System.out.println();
		}
	}
}