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 
template = [3, 1, 4, 2, 5]

template04 = [3, 1, 4, 2, 5]
template12 = [4, 1, 5, 2, 6, 3, 7]
template3 = [3, 1, 4, 2, 6, 8, 5, 7]

count = int(input())
for i in range(count):
    number = int(input())
    res = []
    if number <= 3:
        res.append(-1)
    else:
        copy_count = number // 5
        last_temp = number % 5

        last_template = template
        if last_temp == 0 or last_temp == 4:
            last_template = template04
        elif last_temp == 1 or last_temp == 2:
            last_template = template12
            copy_count -= 1
        else:
            last_template = template3
            copy_count -= 1

        counter = 0
        while counter < copy_count * 5:
            res.append(template[counter % 5] + (counter // 5) * 5)
            counter += 1

        final_counter = 0
        while counter + final_counter < number:
            res.append(last_template[final_counter] + counter)
            final_counter += 1

    for j in range(len(res)):
        print(res[j], end=' ')
    print()