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

def a4(p):
	print(p+1,p+3,p,p+2,end=' ')
def a5(p):
	print(p,p+3,p+1,p+4,p+2,end=' ')
def a6(p):
	print(p,p+3,p+1,p+4,p+2,p+5,end=' ')
def a7(p):
	print(p,p+3,p+1,p+5,p+2,p+4,p+6,end=' ')

def solve(n):
	i=1
	while(n>=8):
		a4(i)
		i+=4
		n-=4
	if n==4:
		a4(i)
	elif n==5:
		a5(i)
	elif n==6:
		a6(i)
	elif n==7:
		a7(i)
	print()
	
def main():
	inp=stdin.readline
	for _ in range(int(inp())):
		n=int(inp())
		if n<=3:
			print(-1)
		else:
			solve(n)

main()