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.*;
import java.util.StringTokenizer;

public class Codeforces {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    static FastReader s = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);

    private static int[] rai(int n) {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextInt();
        }
        return arr;
    }

    private static long[] ral(int n) {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextLong();
        }
        return arr;
    }

    private static int ri() {
        return s.nextInt();
    }

    private static long rl() {
        return s.nextLong();
    }

    private static String rs() {
        return s.next();
    }

    public static void main(String[] args) {
        int t=ri();
        StringBuilder ans=new StringBuilder();
        while(t-->0)
        {
            int n=ri();
            if(n<4)
            {
                ans.append("-1\n");
                continue;
            }
            else if(n==4)
            {
                ans.append("3 1 4 2\n");
                continue;
            }
            else if(n==5)
            {
                ans.append("1 3 5 2 4\n");
                continue;
            }
            else if(n==6)
            {
                ans.append("1 3 5 2 4 6\n");
                continue;
            }
            List<Integer> list=new ArrayList<>();
            for(int i=1;i<=n;i+=2)
            {
                list.add(i);
            }
            List<Integer> list2=new ArrayList<>();
            HashSet<Integer> set=new HashSet<>();
            int val=list.get(list.size()-1);

            val-=3;
//            System.out.println(val);
            while(val>=4)
            {
                list2.add(val);
                set.add(val);
                val-=4;
            }
            list2.add(2);
            set.add(2);
            for(int i=2;i<=n;i+=2)
            {
                if(!set.contains(i))
                {
                    list2.add(i);
                }
            }
            for(int i:list)
            {
                ans.append(i).append(" ");
            }
            for(int i:list2)
            {
                ans.append(i).append(" ");
            }
            ans.append("\n");

        }
        out.print(ans.toString());
        out.flush();
    }
}
