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 
p = dict()
p['go'] = [3, -2, 3, -2, 3]
p[5] = [3, -2, 3, -2]
p[6] = [4, -3, 2, 2, -3]
p[7] = [3, 3, -4, 3, -4, 3]
p[8] = [4, 3, -4, -2, 4, -3, 4]
p[9] = [4, -3, 2, 4, -2, -3, 4, 2]
t = int(input())
for _ in range(t):
    n = int(input())
    if n < 4:
        print('-1')
    elif n == 4:
        print('3 1 4 2')
    else:
        x = 1
        for _ in range(n // 5 - 1):
            for k in p['go']:
                print(x, end=' ')
                x += k
        for k in p[5 + n % 5]:
            print(x, end=' ')
            x += k
        print(x, end=' ')
        print()
