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.Arrays;
import java.util.Scanner;


public class SpecialPermutation {

    int n;

    public SpecialPermutation(int n) {
        this.n = n;
    }

    public static void main(String[] args) {

        Scanner scan = new Scanner(System.in);
        int N = scan.nextInt();
        for (int i = 0; i < N; i++) {
            int n = scan.nextInt();
            SpecialPermutation p = new SpecialPermutation(n);
            System.out.println(p.solve());
        }

    }

    public String solve() {

        if (n == 0 || n == 1 || n == 2 || n == 3) {
            return "-1";
        }

        StringBuilder s = new StringBuilder();
        if (n % 4 == 0) {

            // Split into 4's
            int c = 2;
            while (c <= n) {
                s.append(c);
                s.append(" ");
                c += 2;
                s.append(c);
                s.append(" ");
                c -= 3;
                s.append(c);
                s.append(" ");
                c += 2;
                s.append(c);
                s.append(" ");
                c += 3;
            }


        } else if (n % 4 == 1) {

            // Split into 4's except remaining 1
            int c = 2;
            for (int i = 0; i < n/4 - 1; i++) {
                s.append(c);
                s.append(" ");
                c += 2;
                s.append(c);
                s.append(" ");
                c -= 3;
                s.append(c);
                s.append(" ");
                c += 2;
                s.append(c);
                s.append(" ");
                c += 3;
            }

            s.append(c);
            s.append(" ");
            c += 2;
            s.append(c);
            s.append(" ");
            c -= 3;
            s.append(c);
            s.append(" ");
            c += 2;
            s.append(c);
            s.append(" ");
            c += 2;
            s.append(c);
            s.append(" ");


        } else if (n % 4 == 2) {

            // Split into 4's and 6
            int c = 2;
            for (int i = 0; i < n/4 - 1; i++) {
                s.append(c);
                s.append(" ");
                c += 2;
                s.append(c);
                s.append(" ");
                c -= 3;
                s.append(c);
                s.append(" ");
                c += 2;
                s.append(c);
                s.append(" ");
                c += 3;
            }

            s.append(c);
            s.append(" ");
            c += 3;
            s.append(c);
            s.append(" ");
            c -= 4;
            s.append(c);
            s.append(" ");
            c += 2;
            s.append(c);
            s.append(" ");
            c += 3;
            s.append(c);
            s.append(" ");
            c -= 2;
            s.append(c);
            s.append(" ");

        } else {
            // Split into 4's and 7
            int c = 2;
            for (int i = 0; i < n/4 - 1; i++) {
                s.append(c);
                s.append(" ");
                c += 2;
                s.append(c);
                s.append(" ");
                c -= 3;
                s.append(c);
                s.append(" ");
                c += 2;
                s.append(c);
                s.append(" ");
                c += 3;
            }

            s.append(c);
            s.append(" ");
            c += 3;
            s.append(c);
            s.append(" ");
            c += 2;
            s.append(c);
            s.append(" ");
            c -= 3;
            s.append(c);
            s.append(" ");
            c -= 3;
            s.append(c);
            s.append(" ");
            c += 2;
            s.append(c);
            s.append(" ");
            c += 3;
            s.append(c);
            s.append(" ");
        }

        return s.toString();
    }

}
