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,stdout

t = int(stdin.readline().strip())

p = [
    [3,1,5,2,4],
    [3,1,5,2,4,6],
    [3,1,5,2,6,4,7],
    [3,1,5,2,6,8,4,7],
    [3,1,5,2,6,8,4,7,9]
]

for _ in range(t):
    n = int(stdin.readline().strip())
    a = 0
    A = []
    if n <= 3:
        stdout.write('-1\n')
        continue
    if n == 4:
        stdout.write('3 1 4 2\n')
        continue
    for _ in range(n//5-1):
        for d in p[0]:
            A.append(str(a+d))
        a += 5
    for d in p[n%5]:
        A.append(str(a+d))

    stdout.write(' '.join(A) + '\n')
