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.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.Scanner;

public class hef {
	

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