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 G {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int T = scanner.nextInt();
        for (int t = 1; t <= T; t++) {
            int n = scanner.nextInt();
            permutation(n);
        }
    }

    public static void permutation(int n) {
        if (n < 4) {
            System.out.println("-1");
            return;
        }
        String s = "";
        int c = n/4;
        for (int i = 0; i < c-1; i++) {
            s += 4*i+2 + " ";
            s += 4*i+4 + " ";
            s += 4*i+1 + " ";
            s += 4*i+3 + " ";
        }
        if (n%4 < 2) {
            s += 4*(c-1)+2 + " ";
            s += 4*(c-1)+4 + " ";
            s += 4*(c-1)+1 + " ";
            s += 4*(c-1)+3 + " ";
            if (n%4 == 1) {
                s += n;
            }
        } else if (n%4 == 2) {
            s += 4*(c-1)+2 + " ";
            s += 4*(c-1)+4 + " ";
            s += 4*(c-1)+1 + " ";
            s += 4*(c-1)+5 + " ";
            s += 4*(c-1)+3 + " ";
            s += 4*(c-1)+6 + " ";
        } else {
            s += 4*(c-1)+2 + " ";
            s += 4*(c-1)+4 + " ";
            s += 4*(c-1)+6 + " ";
            s += 4*(c-1)+3 + " ";
            s += 4*(c-1)+1 + " ";
            s += 4*(c-1)+5 + " ";
            s += 4*(c-1)+7 + " ";
        }
        System.out.println(s.trim());
    }
}
