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.*;
import java.math.*;
import java.lang.*;

public class Q7 {
/*
Testcase


 */

    public static StringBuffer solver(FastReader sc) throws IOException {
        StringBuffer ans = new StringBuffer();
        int n = sc.nextInt();
//        ArrayList<Long> arr = new ArrayList<>();
        if(n<4)
            return ans.append(-1);

        Deque<Integer> dq = new LinkedList<>();

        for(int i=2;i<=n;i+=2){
            if(i==2)
                dq.addFirst(4);
            else if(i==4)
                dq.addFirst(2);
            else
                dq.addFirst(i);
        }

        for(int i=1;i<=n;i+=2){
            dq.addLast(i);
        }

        Iterator i = dq.iterator();
        while(i.hasNext()){
            ans.append(i.next()+" ");
        }

        return ans;
    }

    public static void main(String[] args) throws IOException {
        FastReader sc = new FastReader();
        int test = sc.nextInt();

        for (int t = 0; t < test; t++) {
            String val = String.valueOf(solver(sc));
            System.out.println(val);

        }

    }

    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;
        }
    }
}
