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.util.*;

/**
 * 1352G
 */
public class RareCombinatory {
    static HashMap<Integer, Integer[]> map = new HashMap<>();
    public static void main(String[] s){

        map.put(1, new Integer[]{1});
        map.put(2, new Integer[]{-1});
        map.put(3, new Integer[]{-1});
        map.put(4, new Integer[]{3, 1, 4, 2});

        Scanner input = new Scanner(System.in);
        int n = Integer.parseInt(input.nextLine());

        for(int i = 0; i < n; i++)
            System.out.println(getSequence(Integer.parseInt(input.nextLine())));
    }

    public static String getSequence(int amount) {
        if(map.containsKey(amount))
            return replaceRedundant(Arrays.toString(map.get(amount)));

        for(int i = map.size()+1; i <= amount; i++)
            if(i%2 == 0)
                putInMap(i, 1, 0);
            else
                putInMap(i, 0, i-1);

        return replaceRedundant(Arrays.toString(map.get(amount)));
    }

    public static void putInMap(int i, int destPos, int newPos){
        Integer[] array = new Integer[i];
        array[newPos] = i;
        System.arraycopy(map.get(i-1), 0, array, destPos, i-1);
        map.put(i, array);
    }

    public static String replaceRedundant(String s){
        return s.replaceAll("]", "").replaceAll("\\[", "").replaceAll(",", "");
    }
}