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 javafx.util.Pair;

import java.util.*;
import java.io.*;
import java.text.*;
import java.math.*;

public class Main {
    public static FastIO file = new FastIO();

    private static void solve() {
        int amount = nextInt();
        while (amount-- > 0) {
            int length = nextInt();
            int kostyl = length;
            if (length == 3 || length == 1 || length == 0 || length == 2) {
                System.out.println(-1);
                continue;
            }
                if (length % 2 == 0) kostyl -= 1;
            String str = "";
            for (int i = 0; i < length; i += 2) {
                str += kostyl - i + " ";
            }
            str += "4 2 ";
            for (int i = 6; i < length+1; i+=2) {
                str+=i+" ";
            }
            System.out.println(str);
        }
    }

    private static int[] nextArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = nextInt();
        return a;
    }

    public static int[][] nextArray2D(int n, int m) {
        int[][] result = new int[n][];
        for (int i = 0; i < n; i++) {
            result[i] = nextArray(m);
        }
        return result;
    }

    public static long pow(long n, long p) {
        long ret = 1L;
        while (p > 0) {
            if (p % 2 != 0L)
                ret *= n;
            n *= n;
            p >>= 1L;
        }
        return ret;
    }

    public static String next() {
        return file.next();
    }

    public static int nextInt() {
        return file.nextInt();
    }

    public static long nextLong() {
        return file.nextLong();
    }

    public static double nextDouble() {
        return file.nextDouble();
    }

    public static String nextLine() {
        return file.nextLine();
    }

    public static class FastIO {
        BufferedReader br;
        StringTokenizer st;
        PrintWriter out;

        public FastIO() {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }

        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;
        }

    }

    public static void main(String[] args) throws IOException {
        solve();
    }


}

