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 
# f = open("input.txt", "r")
# n = int(f.readline())
# print(n)
n = int(input())

for i in range(0, n):
    # l = f.readline()
    # print('------')
    # print(l)
    l = int(input())
    str_ = ''
    if int(l) <= 3:
        print('-1')
    elif int(l) == 4:
        print('3 1 4 2')
    else:
        k = int(l)
        t = k - (k + 1) % 2
        str_ = str_ + str(t)
        t = t - 2
        while t > 0:
            str_ = str_ + ' ' + str(t)
            t = t - 2
        str_ = str_ + ' 4 2'
        t = 6
        while t <= k:
            str_ = str_ + ' ' + str(t)
            t = t + 2
        print(str_)