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.*;
public class Main {
    public static void main(String args[]) {
        Scanner s = new Scanner(System.in);
        int t = s.nextInt();
        while(t-->0){
            int n = s.nextInt();
            ArrayList<Integer> a = new ArrayList<>();

            a.add(n);

            int l = n - 3;
            while(l > 0){
                a.add(0,l);
                l -= 2;
            }
            int ln = a.size();
            if(ln < 2){
                System.out.println(-1);
                continue;
            }
            a.add(ln - 2, n - 1);
            int r = n - 2;
            while(r > 0){
                a.add(r);
                r -= 2;
            }

            for(int i = 0 ; i < n ; i++)
            System.out.print(a.get(i)+" ");
            System.out.println();
        }
        
    }
}