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 
"""
def f(i, k):
	
	if i < k:
		return "NO"
	elif (i-k+1)%2 == 1 and (i-k+1) > 0:
		l1 = [1]*(k-1)
		l2 = [i-k+1]
		print("YES")
		return l1 + l2
	elif (i-(k-1)*2)%2 == 0 and (i-(k-1)*2) > 0:
		l1 = [2]*(k-1)
		l2 = [i-(k-1)*2]
		print("YES")
		return l1 + l2
	else:
		return "NO"
"""
"""
def f2(n, k):
	need = (k-1)//(n-1)
	print(need+ k)
"""
"""
def fD(arr):
	lsum = 0
	count = 0
	alice = 0
	bob = 0
	start = 0
	end = len(arr) - 1
	while start <= end:
		candy = 0
		if count%2 == 0:
			#print(lsum, candy)
			while lsum >= candy and start <= end:
				candy += arr[start]
				start += 1
			alice += candy
			lsum = candy
			count += 1

		elif count%2 != 0:
			while lsum >= candy and start <= end:
				candy += arr[end]
				end -= 1
			bob += candy
			lsum = candy
			count += 1

	return count, alice, bob
"""
"""
def fF(a, b, c):
	s = ""
	if (b != 0 or c != 0):
		s = "1"
	else:
		s = "0"
	for i in range(b):
		if i%2 == 0:
			s += "0"
		else:
			s += "1"
	for j in range(len(s)):
		if s[j] == "0":
			s = s[:j] + "0"*a + s[j:]
			break
	for j in range(len(s)):
		if s[j] == "1":
			s = s[:j] + "1"*c + s[j:]
			break
	
	print(s)

"""

def fG(k):
	r = []
	if k < 4:
		print(-1)
		return
	for i in range(1,k+1,2):
		r.append(i)
	r = r[::-1]
	r = r + [4, 2]
	for i in range(6, k+1, 2):
		r.append(i)
	return (r)

n = int(input())
for i in range(n):
	#k = int(input())
	#l = list(map(int, input().split()))
	r = fG(int(input()))
	#r = fF(l)
	if r != None:
		for j in r:
			print(j, end = " ")