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 
// package com.company;

import java.io.*;
import java.util.ArrayList;
import java.util.StringTokenizer;

//****Use Integer Wrapper Class for Arrays.sort()****
public class CX7 {
    static PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));

    public static void main(String[] Args) {
        FastReader scan = new FastReader();
        int t = 1;
        t = scan.nextInt();
        while (t-- > 0) {
            int n = scan.nextInt();
            if (n < 4) {
                out.println(-1);
            } else {
                ArrayList<Integer> al=new ArrayList<>();
                al.add(n);
                int nl=n-2;
                while(nl>=1){
                    al.add(nl);
                    nl-=2;
                }
                ArrayList<Integer> ar=new ArrayList<>();
                ar.add((n-3));
                ar.add((n-1));
                int nr=n-5;
                while(nr>=1){
                    ar.add(nr);
                    nr-=2;
                }
                for(int i=ar.size()-1;i>=0;i--){
                    out.print(ar.get(i)+" ");
                }
                for(int i=0;i<al.size();i++){
                    out.print(al.get(i)+" ");
                }
                out.println();
            }
        }
        out.flush();
        out.close();
    }

    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;
        }
    }

}
