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 
//package godiji;

import java.util.Scanner;
import java.util.Stack;
import java.util.TreeMap;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.PriorityQueue;

public class pac1 {
	static Scanner scn = new Scanner(System.in);
	// static int count = 0;

	public static void main(String[] args) throws Exception {
		int t = scn.nextInt();
		while (t-- > 0) {
			int n = scn.nextInt();
			if (n == 2 || n == 3)
				System.out.println("-1");
			else {
				StringBuilder sb = new StringBuilder();
				int s = n, a = 2;
				if (n % 2 == 0) {
					s = n - 1;
					while (s >= 1) {
						sb.append(s + " ");
						s -= 2;
					}
					sb.append(4 + " ");
					while (a <= n) {
						if (a != 4)
							sb.append(a + " ");
						a += 2;
					}
				} else {
					while (s >= 1) {
						sb.append(s + " ");
						s -= 2;
					}
					sb.append(4 + " ");
					while (a <= n) {
						if (a != 4)
							sb.append(a + " ");
						a += 2;
					}
				}
				System.out.println(sb.toString());
			}
		}

	}

	public static int palin(String str) {
		int n = str.length(), count = 0;

		for (int i = 0; i < n / 2; i++) {
			if (str.charAt(i) != str.charAt(n - i - 1)) {
				count++;
			}
		}
		return count;
	}

	public static long gcd(long a, long n) {

		if (a == 0)
			return n;
		return gcd(n % a, a);
	}
}

class pair {
	int x;
	int y;

	pair(int a, int b) {
		this.x = a;
		this.y = b;
	}
}

class sorting implements Comparator<pair> {

	@Override
	public int compare(pair o1, pair o2) {
		// TODO Auto-generated method stub

		int a = Math.max(o1.x, o2.x), b = o1.y - o2.y;
		if (b > 0)
			return -1;
		else
			return 0;
	}

}
