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;

public class Main {
	
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t= Integer.parseInt(br.readLine());
		
		while(t!=0) {
			t--;
			
			int n= Integer.parseInt(br.readLine());
			if(n<=3) {
				System.out.println("-1");
			}else {
				int r[];
				r = calculateVal(n);
				for(int i=0;i<n;i++) {
					System.out.print(r[i]+" ");
				}
				System.out.println();
			}
		}
	}
	
	public static int[] calculateVal(int n) {
		int result[] = new int[n];
		int start=0; int end =n-1;
		for(int i=n;i>=1;i--) {
			if(i%2!=0) {
				result[start]= i;
				start++;
			}else {
				result[end]=i;
				end--;
			}
		}
		int t= result[start];
		result[start] = result[start+1];
		result[start+1]=t;
		return result;
	}
}