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 int[] constructSpecialPermutation(int n) {
        int[] permutation = new int[n];
        int oddStart = n % 2 == 0 ? n-1 : n;
        int i = 0;
        for (int odd=oddStart; odd >= 1; i++, odd-=2)
            permutation[i] = odd;
        if (i < n) {
            permutation[i] = 4;
            if (i + 1 < n)
                permutation[i+1] = 2;
        }
        i = i + 2;
        for (int even=6; i < n; i++, even+=2)
            permutation[i] = even;

        for (i = 0; i < n; i++) {
            if (permutation[i] > n)
                return null;
            if (i == 0)
                continue;
            int diff = Math.abs(permutation[i] - permutation[i-1]);
            if (diff < 2 ||  diff > 4)
                return null;
        }

        return permutation;
    }

    public static void main(String[] args) {
        Main main = new Main();
        Scanner sc = new Scanner(System.in);
        int tests = sc.nextInt();
        for (int t = 0; t < tests; t++) {
            int n = sc.nextInt();
            int[] permutation = main.constructSpecialPermutation(n);
            if (permutation == null || permutation.length == 0)
                System.out.println("-1");
            else {
                for (int i = 0; i < permutation.length; i++) {
                    System.out.print(permutation[i] + " ");
                }
                System.out.println();
            }
        }
    }
}