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 
T = int(input())

for t in range(T):
  a = int(input())
  if a <= 3:
    print('-1')
    continue
  if a%4 == 0: now = [2,4,1,3]
  elif a%4 == 1: now = [3, 1, 5, 2, 4]
  elif a%4 == 2: now = [1, 4, 2, 6, 3, 5 ]
  elif a%4 == 3: now = [5, 1, 3, 6, 2, 4, 7 ]
  a -= a%4
  a -= 4
  v = len(now)+1
  for i in range(a//4):
    now.extend([v+1,v+3,v,v+2])
    v += 4
  ans = ''
  for c in now: ans+=str(c)+' '
  ans = ans[:-1]
  print(ans)
