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 sys

def minp():
	return sys.stdin.readline().strip()

def mint():
	return int(minp())

def mints():
	return map(int, minp().split())

def rec(a, n, was):
	if n == len(a):
		print(True)
		return True
	v = a[n-1]
	#for i in range(max(v-4,1), min(v+5, len(a))):
	for i in [v+2,v-4,v+3,v-3,v+4,v-2]:
		if i < 1 or i > len(a):
			continue
		if abs(i-v) > 1 and not was[i]:
			a[n] = i
			was[i] = 1
			if rec(a, n+1, was):
				return True
			was[i] = 0
			a[n] = 0
	return False

def solve_stupid():
	n = mint()
	ok = False
	for i in range(1,n+1):
		x = [i]*n
		was = [0]*(n+1)
		was[i] = 1
		if rec(x, 1, was):
			ok = True
			break
	if ok:
		print("YES")
		print(x)
	else:
		print("NO")

def solve():
	n = mint()
	if n < 4:
		print(-1)
		return
	a = []
	for i in range(1,n+1,2):
		a.append(i)
	x = a[-1]
	a.append(x-3)
	if n % 2:
		a.append(x-1)
	else:
		a.append(x+1)
		a.append(x-1)
	for i in range(x-5, 0, -2):
		a.append(i)
	#print(n)
	if n == 4:
		a = [2, 4, 1, 3]
	print(*a)


for i in range(mint()):
	solve()
