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 
# 1
# No
# No
# 2 4 1 3
# 1 3 5 2 4 - nice
# 1 3 5 2 4 6
# 1 3 6 2 4 7 5

# v%5==0 : 1 3 5 2 4 - nice
# v%5==1 : 1 3 5 2 4 6
# v%5==2 : 1 3 6 2 4 7 5
# v%5==3 : 1 3 6 2 4 7 5 8
# v%5==4 : 1 3 6 2 4 8 5 7 9

def parse(s):
    return [int(n) for n in s.split(' ')]

magic = [
    parse('1 3 5 2 4'),
    parse('1 3 5 2 4 6'),
    parse('1 3 6 2 4 7 5'),
    parse('1 3 6 2 4 7 5 8'),
    parse('1 3 6 2 4 8 5 7 9')
]

for t in range(int(input())):
    n = int(input())
    if n == 1:
        ans = [1]
    elif n <= 3:
        ans = None
    elif n == 4:
        ans = [2, 4, 1, 3]
    else:
        mod = 5
        extra = 0
        rest = n
        ans = []
        while rest >= 2 * mod:
            ans += [v+extra for v in magic[0]]
            extra += mod
            rest -= mod
        ans += [v+extra for v in magic[rest%mod]]

    if ans is None:
        print(-1)
    else:
        print(' '.join(str(v) for v in ans))
        