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.*;

public class Solution {

    public void solve() {
        for (int test = reader.nextInt(); test > 0; test--) {
            int n = reader.nextInt();
            int[] a = find(n);
            if (a == null) writer.println(-1);
            else {
                for (int i = 0; i < n; i++) writer.print(a[i] + " ");
                writer.println();
            }
        }
    }

    int[] find(int n) {
        if (n <= 3) return null;
        if (n == 4) return new int[]{3, 1, 4, 2};

        int[] a = new int[n];

        if (n % 2 == 1) {
            int cnt = 0;
            for (int i = 1; i <= n; i += 2) {
                a[cnt++] = i;
            }

            a[cnt++] = n - 3;
            a[cnt++] = n - 1;

            int x = n - 5;
            while (x > 0) {
                a[cnt++] = x;
                x -= 2;
            }

            return a;
        }

        int cnt = 0;
        for (int i = 1; i <= n-1; i += 2) {
            a[cnt++] = i;
        }

        a[cnt++] = n-4;
        a[cnt++] = n;
        a[cnt++] = n-2;

        int x = n-6;
        while (x > 0) {
            a[cnt++] = x;
            x -= 2;
        }

        return a;
    }

    private InputReader reader;
    private PrintWriter writer;

    public Solution(InputReader reader, PrintWriter writer) {
        this.reader = reader;
        this.writer = writer;
    }

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

        Solution solution = new Solution(reader, writer);
        solution.solve();

        writer.flush();
    }

    static class InputReader {
        private static final int BUFFER_SIZE = 1 << 20;

        private BufferedReader reader;
        private StringTokenizer tokenizer;

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

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

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

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

