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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.List;

public class SpecialPermutation { // Template for CF
    public static class ListComparator implements Comparator<List<Integer>> {

        @Override
        public int compare(List<Integer> l1, List<Integer> l2) {
            for (int i = 0; i < l1.size(); ++i) {
                if (l1.get(i).compareTo(l2.get(i)) != 0) {
                    return l1.get(i).compareTo(l2.get(i));
                }
            }
            return 0;
        }
    }

    public static void main(String[] args) throws IOException {
        // Check for int overflow!!!!
        // Should you use a long to store the sum or smthn?
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        int T = Integer.parseInt(f.readLine());
        for (int i = 0; i < T; i++) {
            int N = Integer.parseInt(f.readLine());
            if (N <= 3) {
                out.println(-1);
            } else {
                List<Integer> list = new ArrayList<>(N);
                if (N % 2 == 0) {
                    int ind = N - 1;
                    while (ind >= 1) {
                        list.add(ind);
                        ind -= 2;
                    }
                    list.add(4);
                    list.add(2);
                    ind = 6;
                    while (ind <= N) {
                        list.add(ind);
                        ind += 2;
                    }
                } else {
                    int ind = N;
                    while (ind >= 1) {
                        list.add(ind);
                        ind -= 2;
                    }
                    list.add(4);
                    list.add(2);
                    ind = 6;
                    while (ind <= N) {
                        list.add(ind);
                        ind += 2;
                    }
                }
                for (int j = 0; j < list.size(); j++) {
                    out.print(list.get(j) + " ");
                }
                out.println();
            }
        }
        out.close();
    }

}