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
import math
import operator as op
from functools import reduce

def read_line():
	return sys.stdin.readline()[:-1]
 
def read_int():
	return int(sys.stdin.readline())
	
def read_int_line():
	return [int(v) for v in sys.stdin.readline().split()]

def read_float_line():
	return [float(v) for v in sys.stdin.readline().split()]

def ncr(n, r):
    r = min(r, n-r)
    numer = reduce(op.mul, range(n, n-r, -1), 1)
    denom = reduce(op.mul, range(1, r+1), 1)
    return numer / denom

t = read_int()
for i in range(t):
	n = read_int()
	if n<4:
		print(-1)
	else:
		ans = []
		if n&1!=0:
			for i in range(1,n+1):
				if i&1!=0:
					ans.append(i)
			ans.append(n-3)
			ans.append(n-1)
			for i in range(n-5,0,-1):
				if i&1==0:
					ans.append(i)
			print(*ans)
		else:
			for i in range(1,n+1):
				if i&1==0:
					ans.append(i)
			ans.append(n-3)
			ans.append(n-1)
			for i in range(n-5,0,-1):
				if i&1!=0:
					ans.append(i)
			print(*ans)

