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 
from sys import stdin, exit
input = stdin.readline

def i(): return input()
def ii(): return int(input())
def iis(): return map(int, input().split())
def liis():	return list(map(int, input().split()))
def print_array(a): print(" ".join(map(str, a)))

t = ii()
for _ in range(t):
	n = ii()	
	if n < 4: print(-1)
	else:
		a = []
		for i in range(2, n+1):
			if i%2 != 0: continue
			a.append(i)
		for i in range(n, -1, -1):
			if i%2 != 1: continue
			a.append(i)
		for i in range(n):
			if abs(a[i]-a[i+1]) < 2:
				if a[i] > a[i+1]:
					a[i-1], a[i], a[i+1], a[i+2] = a[i+1], a[i+2], a[i], a[i-1]
				else:
					a[i-1], a[i], a[i+1], a[i+2] = a[i+2], a[i+1], a[i-1], a[i]
				break
		print_array(a)
