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 
seq = [1, 3, 5, 2, 4, 6, 8, 10, 7, 9]
after = [
    [1],
    [1, 'l', 2],
    [1, 3, 'l', 2],
    [1, 3, 'l', 2, 4],
    [1, 3, 5, 2, 4],
    [1, 3, 5, 2, 4, 6],
    [1, 5, 2, 6, 3, 7, 4],
    [1, 5, 2, 6, 3, 7, 4, 8],
    [1, 3, 5, 2, 4, 7, 9, 6, 8]
]
base = [
    [-1],
    [-1],
    [-1],
    [2, 4, 1, 3],
    [1, 3, 5, 2, 4],
    [1, 3, 5, 2, 4, 6],
    [1, 5, 2, 6, 3, 7, 4],
    [1, 5, 2, 6, 3, 7, 4, 8],
    [1, 3, 5, 2, 4, 7, 9, 6, 8]
]

def check(ans):
    for i in range(1, len(ans)):
        if not (2 <= abs(ans[i-1] - ans[i]) <= 4):
            print('EXCEPT', len(ans), ans)
            exit(0)

for _ in range(int(input())):
    n = int(input())
    ans = []
    left = n % 10
    start = 10 * (n // 10)
    if start == 0:
        # check(base[n-1])
        print(*base[n-1])
        continue
    for i in range(n - left):
        ans.append(seq[i % 10] + 10 * (i // 10))
    if left == 0:
        # check(ans)
        print(*ans)
        continue

    toadd = [start + x if x != 'l' else ans.pop() for x in after[left-1]]
    ans.extend(toadd)
    # check(ans)
    print(*ans)