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 Main {

    public static void main(String[] args) {
        
        Scanner sc = new Scanner(System.in);
        
        int T = Integer.parseInt(sc.next());
        StringBuilder sb = new StringBuilder();
        for(int t = 0; t < T; t++){
            int n = Integer.parseInt(sc.next());
            if(n <= 3){
                sb.append(-1);
            }else{
                if(n%2 == 0){
                    for(int i = n-1; i > 0; i -= 2){
                        sb.append(i).append(" ");
                    }
                }else{
                    for(int i = n; i > 0; i -= 2){
                        sb.append(i).append(" ");
                    }
                }
                sb.append("4 2 ");
                for(int i = 6; i <= n; i += 2){
                    sb.append(i).append(" ");
                }
            }
            sb.append(System.lineSeparator());
        }
        System.out.print(sb);
    }
}