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.math.*;
import java.util.*;





public class Main {

    static MyScanner in = new MyScanner();
    static   PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
    int N;
    static int [] dr = {1,-1,0,0};
    static int [] dc={0,0,-1,1};
    static boolean [][] grid;
    static int [] bishopr = {-1,1,-1,1};
    static int [] bishopc = {1,1,-1,-1};
    static long H,W;
    static BitSet bs;
    static int mod = 1000000007;
    static int max = 10*100;
    static int BIT[]  = new int [max+1];
    static HashMap<Integer,Integer> map =new HashMap<>();
    static int cnt=1;
    public static void main(String args[]) throws IOException {
        int t = in.nextInt();
        while(t-->0){
            int n = in.nextInt();
            if(n<4){
                out.println(-1);
            }
            else{
                for(int i=n;i>=1;i--){
                    if((i&1)==1){
                            out.print(i+" ");
                    }
                }
                out.print(4+" "+2+" ");
                for(int i=6;i<=n;i+=2){
                    out.print(i+" ");
                }
                out.print("\n");
            }
        }
        out.flush();
    }
        
       static int gcd(int a, int b){
        return b!=0?gcd(b, a%b):a;
    }

        static boolean isEven(long a) {
            return (a&1)==0;
        }
    
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
   
        public MyScanner() {
           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;
        }
  
     }
}