Problem: You are given a positive integer n, it is guaranteed that n is even (i.e. divisible by 2).

You want to construct the array a of length n such that: 

  * The first n/2 elements of a are even (divisible by 2); 
  * the second n/2 elements of a are odd (not divisible by 2); 
  * all elements of a are distinct and positive; 
  * the sum of the first half equals to the sum of the second half (∑_{i=1}^{n/2} a_i = ∑_{i=n/2 + 1}^{n} a_i). 



If there are multiple answers, you can print any. It is not guaranteed that the answer exists.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The only line of the test case contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of the array. It is guaranteed that that n is even (i.e. divisible by 2).

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — "NO" (without quotes), if there is no suitable answer for the given test case or "YES" in the first line and any suitable array a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) satisfying conditions from the problem statement on the second line.

Example

Input


5
2
4
6
8
10


Output


NO
YES
2 4 1 5
NO
YES
2 4 6 8 1 3 5 11
NO

Solution (in PYTHON3):

Solution:
for _ in range(int(input())):
  n, k = map(int, input().split())
  data = list(map(int, input().split()))
  
  in_map = {}
  out_map = {}
  temp_map = {}
  from_0 = set()

  for i in range(n // 2):
    min_value = min(data[i], data[n - i - 1])
    max_value = max(data[i], data[n - i - 1])
    lower_bound = min_value + 1
    higher_bound = max_value + k
    now_sum = min_value + max_value
    if lower_bound in in_map:
      in_map[lower_bound] += 1
    else:
      in_map[lower_bound] = 1
    if higher_bound in out_map:
      out_map[higher_bound] -= 1
    else:
      out_map[higher_bound] = -1
    if now_sum in temp_map:
      temp_map[now_sum] += 1
    else:
      temp_map[now_sum] = 1
    from_0.add(lower_bound)
    from_0.add(higher_bound)
    from_0.add(now_sum)
  
  sorted_set = sorted(from_0)

  my_sum = 0
  result = n

  for i in sorted_set:
    a = 0
    if i in in_map:
      a = in_map[i]
    my_sum += a
    t = 0
    if i in temp_map:
      t = temp_map[i]
    now_total = n - (my_sum + t)
    result = min(result, now_total)
    b = 0
    if i in out_map:
      b = out_map[i]
    my_sum += b
  
  print(result)