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 
"""
Please FUCKING

      ***   *       *   *********        ***   *       *     ***
    **      *       *   *              **      *     **      ***
  **        *       *   *            **        *   **        ***
**          *********   *********  **          ***           ***
  **        *       *   *            **        *   **
    **      *       *   *              **      *     **      ***
      ***   *       *   *********        ***   *       *     ***

check 1: ok
check 2: ok
check 3: ok
"""
from sys import stdin


def inp():
    return stdin.buffer.readline().rstrip().decode("utf8")


def itg():
    return int(stdin.buffer.readline())


def mpint():
    return map(int, stdin.buffer.readline().split())

# for even n >= 4
# all even and end with 4 + increasing odd
# e.g.
# (4): 2 4 (1 3)
# (6): 6 2 4 (1 3 5)
# (8): 8 6 2 4 (1 3 5 7) and so on

# for odd n >= 5
# (5): 2 4 (1 3 5)
# (7): 6 2 4 (1 3 5 7)
# (9): 8 6 2 4 (1 3 5 7 9)

from collections import deque

for case in range(itg()):
    n = itg()
    if n <= 3:
        print(-1)
        continue
    ans = deque([2, 4])
    for i in range(6, n+1, 2):
        ans.appendleft(i)

    for i in range(1, n+1, 2):
        ans.append(i)

    print(*ans)

# Please FUCKING check!
