Problem: You are given an array a consisting of n integers (it is guaranteed that n is even, i.e. divisible by 2). All a_i does not exceed some integer k.

Your task is to replace the minimum number of elements (replacement is the following operation: choose some index i from 1 to n and replace a_i with some integer in range [1; k]) to satisfy the following conditions:

  * after all replacements, all a_i are positive integers not greater than k; 
  * for all i from 1 to n/2 the following equation is true: a_i + a_{n - i + 1} = x, where x should be the same for all n/2 pairs of elements. 



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 first line of the test case contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 2 ⋅ 10^5) — the length of a and the maximum possible value of some a_i correspondingly. It is guratanteed that n is even (i.e. divisible by 2). The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ k), where a_i is the i-th element of a.

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

Output

For each test case, print the answer — the minimum number of elements you have to replace in a to satisfy the conditions from the problem statement.

Example

Input


4
4 2
1 2 1 2
4 3
1 2 2 1
8 7
6 1 1 7 6 3 4 6
6 6
5 2 6 1 3 4


Output


0
1
4
2

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)