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.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class G {
    public static void main(String[] args) throws IOException {
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        InputReader in=new InputReader(System.in);
        int t=in.nextInt();
        while (t-->0) {
            int n=in.nextInt();
            boolean []visit=new boolean[n];
            visit[0]=true;
            if(n<=3) out.println(-1);
            else{
                int []a=new int[]{2,4,1,3};
                int start=0;
                List<Integer> list=new ArrayList<>();
                while (start<n&&(start+8<n||(n-start)%4==0||n-start==5)){
                    start+=4;
                    for(int x:a) list.add(x);
                    a[0]=start+2;
                    a[1]=start+4;
                    a[2]=start+1;
                    a[3]=start+3;
                }
                int remain=n-start;
                switch (remain){
                    case 6:
                        list.add(start+1);
                        list.add(start+4);
                        list.add(start+2);
                        list.add(start+5);
                        list.add(start+3);
                        list.add(start+6);
                        break;
                    case 7:
                        list.add(start+1);
                        list.add(start+5);
                        list.add(start+2);
                        list.add(start+6);
                        list.add(start+3);
                        list.add(start+7);
                        list.add(start+4);
                        break;
                    case 1:
                        list.add(n);
                }
                for(int x:list) out.print(x+" ");
                out.println();
            }
        }
        out.flush();
    }
    static class InputReader{
        private BufferedReader in;
        private StringTokenizer tokenizer;
        public InputReader(InputStream stream){
            in = new BufferedReader(new InputStreamReader(stream),32768);
            tokenizer = null;
        }
        public String next() throws IOException{
            while(tokenizer==null || !tokenizer.hasMoreTokens()){
                tokenizer = new StringTokenizer(in.readLine());
            }
            return tokenizer.nextToken();
        }
        public Long nextLong() throws IOException {
            String next = next();
            return Long.valueOf(next);
        }
        public int nextInt() throws IOException{
            return Integer.valueOf(next());
        }
    }
}