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.*;
import java.util.*;


/**
 * Created by Katushka on 11.03.2020.
 */
public class B {
    final static long MOD = 998244353;

    static int[] readArray(int size, InputReader in) {
        int[] a = new int[size];
        for (int i = 0; i < size; i++) {
            a[i] = in.nextInt();
        }
        return a;
    }


    static long[] readLongArray(int size, InputReader in) {
        long[] a = new long[size];
        for (int i = 0; i < size; i++) {
            a[i] = in.nextLong();
        }
        return a;
    }

    static long[] getPartialSums(int[] a) {
        if (a.length == 0) {
            return new long[]{};
        }
        long[] res = new long[a.length];
        res[0] = a[0];

        for (int i = 1; i < a.length; i++) {
            res[i] = res[i - 1] + a[i];
        }

        return res;
    }

    public static void main(String[] args) throws FileNotFoundException {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

        int t = in.nextInt();
        for (int ii = 0; ii < t; ii++) {
            int n = in.nextInt();
            if (n <= 3) {
                out.println(-1);
                continue;
            }
            boolean start3 = false;
            StringBuilder ans = new StringBuilder();
            int k = 0;
            if (n % 4 == 0) {
                k = 0;
            } else if (n % 4 == 1) {
                k = 5;
                ans.append("1 4 2 5 3 ");
            } else if (n % 4 == 2) {
                ans.append("1 4 2 6 3 5 ");
                k = 6;
            } else {
                ans.append("7 4 2 6 3 1 5 ");
                k = 7;
            }
            n -= k;
            while (n > 0) {
                if (start3) {
                    ans.append(k + 3).append(' ').append(k + 1).append(' ')
                            .append(k + 4).append(' ').append(k + 2).append(' ');
                } else {
                    ans.append(k + 2).append(' ').append(k + 4).append(' ')
                            .append(k + 1).append(' ').append(k + 3).append(' ');
                }
                n -= 4;
                k += 4;
                start3 = !start3;
            }
            out.println(ans);
        }


        out.close();
    }


    private static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public String nextString() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

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

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

        public char nextChar() {
            return next().charAt(0);
        }
    }
}
