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 io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
import sys

# sys.stdout.write(str(n)+"\n")
p6 = [0, 3, 1, 5, 2, 4]
p7 = [4, 0, 2, 5, 1, 3, 6]
p4 = [1, 3, 0, 2]

t = int(input())
for _ in range(t):
	n = int(input())

	if n <= 3:
		print(-1)
	else:
		next_ = 1

		if n % 4 == 1:
			sys.stdout.write(str(next_) + " ")
			next_ += 1
			n -= 1
		elif n % 4 == 2:
			for i in range(6):
				sys.stdout.write(str(next_ + p6[i]) + " ")
			next_ = 7
			n -= 6 
		elif n % 4 == 3:
			for i in range(7):
				sys.stdout.write(str(next_ + p7[i]) + " ")
			next_ = 8
			n -= 7
		while n > 0:
			for i in range(4):
				sys.stdout.write(str(next_ + p4[i]) + " ")
			next_ += 4
			n -= 4
		sys.stdout.write("\n")
