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 
//Created by Aminul on 5/9/2020.

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

import static java.lang.Math.*;

public class G {
    public static void main(String[] args) throws Exception {
        Scanner in = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int test = in.nextInt();
        for (int t = 1; t <= test; t++) {
            int n = in.nextInt();
            List<Integer> g = solve(n);
            if (g == null) pw.println(-1);
            else {
                for (int i : g) pw.print(i + " ");
                pw.println();
            }

        }

        pw.close();
    }

    static List<Integer> solve(int n) {
        if (n < 4) return null;
        if (n == 4) {
            List<Integer> g = new ArrayList<>();
            g.add(3);
            g.add(1);
            g.add(4);
            g.add(2);
            return g;
        }
        boolean f[] = new boolean[n + 1];
        int even = n - 3;
        List<Integer> g = new ArrayList<>();
        for (int i = 1; i <= n; i += 2) {
            f[i] = true;
            even = i - 3;
            g.add(i);
        }

        if (even > 0) {
            f[even] = true;
            g.add(even);
        }
        even += 4;
        if (even > n) {
            even -= 2;
        }
        while (g.size() < n) {
            if (!f[even]) {
                g.add(even);
                f[even] = true;
            }
            even -= 2;
        }
        return g;
    }

    static void debug(Object... obj) {
        System.err.println(Arrays.deepToString(obj));
    }
}