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.util.*;
import java.io.*;

public class Main {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        Task task = new Task();
        task.solve(in, out);
        out.close();
    }
    // main solver

    static class Task {
        static int[] candies = new int[1001];
        public void solve(InputReader in, PrintWriter out) {
            int test = in.nextInt();
            int i, j;
            int[] steps = {3, 1, 4, 2, 5};
            for (i = 0; i < test; i++) {
                int n = in.nextInt();
                if (n <= 3){
                    out.println(-1);
                }
                else if (n == 4){
                    out.println("3 1 4 2");
                }
                else{
                    ArrayList<Integer> all = new ArrayList<>();
                    all.add(3); all.add(1); all.add(4); all.add(2);
                    boolean back = true;
                    for (int d = 5; d <= n; d++){
                        if (back){
                            all.add(d);
                        }
                        else{
                            all.add(0, d);
                        }
                        back = !back;
                    }
                    for (int d : all){
                        out.print(d + " ");
                    }
                    out.println();
                }
            }
        }
    }
    // fast input reader class;
    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
        }

        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                String line = null;
                try {
                    line = br.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (line == null) {
                    return null;
                }
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        public long nextLong(){
            return Long.parseLong(nextToken());
        }
    }
}