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

__author__ = 'ratmir'

from collections import deque

alphabet = "abcdefghijklmnopqrstuvwxyz"


def solve(n, a, graph):
    return 1


def execute():
    [t] = [int(x) for x in sys.stdin.readline().split()]
    results = []
    for ti in range(0, t):
        [n] = [int(x1) for x1 in sys.stdin.readline().split()]
        res = getRes(n)
        if len(res)==0:
            results.append("-1")
        else:
            results.append(''.join('{} '.format(k) for k in res))

    print(''.join('{}\n'.format(k) for k in results))


def getRes(n):
    if n<4:
        return []
    res = [3, 1, 4, 2]
    while len(res)<n:
        if len(res)%2==0:
            res = [res[0]+2] + res
        else:
            if len(res)==5:
                res = res + [6]
            else:
                res = res + [res[-1] + 2]
    return res


#for n0 in range(0, 10):
#    print getRes(n0)
    #selfcheck(res, n0, n1, n2)

execute()
