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 codechef; // don't place package name! */


import java.io.*;
import java.util.*;
import java.lang.*;
public class permutation{
    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        FastScanner(InputStream stream) {
            try {
                br = new BufferedReader(new
                    InputStreamReader(stream));
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine() {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
     }
	public static void main(String args[]) {
		//try {
			FastScanner sc=new FastScanner(System.in);
			int tests=sc.nextInt();
			for(int l=0;l<tests;l++) {
                int n=sc.nextInt();
                int ar[]=new int[n];
                int a[]=new int[n];
                for(int i=0;i<n;i++){
                    ar[i]=i+1;
                }
                if(n<=3){
                    System.out.println(-1);
                }
                else{
                        
                        int i=1;
                        if(n%2!=0)
                            i=0;
                        int j=0;
                        while(j<n){
                            while(i<n){
                            a[j]=ar[i];
                            i+=2;
                            j++;
                            }
                            a[j]=ar[n-4];
                            j++;
                            a[j]=ar[n-2];
                            i=n-6;
                            j++;
                            while(i>=0){
                                a[j]=ar[i];
                                i-=2;
                                j++;
                            }
                        }
                      for(int h=0;h<n;h++) {
                    	  System.out.print(a[h]+" ");
                      }  System.out.println();
                    
                    
                  
                }
			}
		//}
		//catch(Exception e) {}
	
}
}

