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 SpecialPermutation {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int T = in.nextInt();
        for (int t = 0; t < T; t++) {
            int N = in.nextInt();
            if (N < 4) {
                System.out.println(-1);
            } else {
                ArrayList<Integer> res = new ArrayList<>();
                int current = N % 2 == 0 ? 2 : 1;
                while (current <= N) {
                    res.add(current);
                    current += 2;
                }
                current -= 5;
                res.add(current);
                current += 2;
                res.add(current);
                current -= 4;
                while (current > 0) {
                    res.add(current);
                    current -= 2;
                }
                for (int i = 0; i < N; i++) {
                    System.out.print(res.get(i) + (i == N - 1 ? "\n" : " "));
                }
            }
        }
    }
}