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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.*;

public class practiceJAVA{
    static int count=0;

    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        int t=Reader.nextInt();
        for(int i=0;i<t;i++){
            int n=Reader.nextInt();
            if(n<4){
                System.out.println(-1);
                continue;
            }
            LinkedList<Integer> l = new LinkedList<>();
            l.addLast(3);
            l.addLast(1);
            l.addLast(4);
            l.addLast(2);
            for(int j=5;j<=n;j++){
                if(j-l.peekLast()>=2){
                    l.addLast(j);
                }
                else{
                    l.addFirst(j);
                }
            }
            Iterator itr = l.iterator();
            while(itr.hasNext()){
                System.out.print(itr.next()+" ");
            }
            System.out.println();
        }
        
    } // main end
} // class end

class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            tokenizer = new StringTokenizer(
                    reader.readLine() );
        }
        return tokenizer.nextToken();
    }
    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }
}