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.ArrayList;
import java.util.Collections;
import java.util.Scanner;

public class abc {

	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner s = new Scanner(System.in);

		int tt = s.nextInt();

		for (int pp = 0; pp < tt; pp++) {

			int n = s.nextInt();

			if (n <= 3) {
				System.out.println(-1);
			} else {
				ArrayList<Integer> even = new ArrayList<Integer>();
				ArrayList<Integer> odd = new ArrayList<Integer>();
				if (n % 2 == 0) {
					for (int i = 2; i <= n; i += 2) {
						even.add(i);
					}
					for (int i = 1; i <= n - 1; i += 2) {
						odd.add(i);
					}

					Collections.swap(odd, odd.size() - 1, odd.size() - 2);
					Collections.reverse(odd);
					even.addAll(odd);
					for (int i = 0; i < even.size(); i++) {
						System.out.print(even.get(i) + " ");
					}
					System.out.println();
					
				} else {
					for (int i = 1; i <= n; i += 2) {
						odd.add(i);
					}
					for (int i = 2; i <= n - 1; i += 2) {
						even.add(i);
					}

					Collections.swap(even, even.size() - 1, even.size() - 2);
					Collections.reverse(even);
					odd.addAll(even);
					for (int i = 0; i < odd.size(); i++) {
						System.out.print(odd.get(i) + " ");
					}
					System.out.println();
				}
			}

		}
	}

}
