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:
t = int(input())

while t:
  n,k = map(int,input().split())
  li = list(map(int,input().split()))
  one_counts = [0]*(2*k+5)
  pairs_array = []
  for i in range(len(li)//2):
    pairs_array.append([min(li[i],li[n-i-1]),max(li[i],li[n-i-1])])
  zero_counts = {}

  for pair in pairs_array:
    lower_bound = pair[0] + 1
    upper_bound = pair[1] + k
    if not zero_counts.get(pair[0] + pair[1]):
      zero_counts[pair[0] + pair[1]]=1
    else:
      zero_counts[pair[0] + pair[1]]+=1
    one_counts[lower_bound]+=1
    one_counts[upper_bound+1]-=1

  for i in range(1,len(one_counts)):
    one_counts[i] = one_counts[i] + one_counts[i-1]

  min_nums = n
  for i in range(2,2*k+1):
    total_sum = i
    zero_changes = 0
    if zero_counts.get(i):
      zero_changes = zero_counts[i]
    one_changes = one_counts[i] - zero_changes
    two_changes = (n//2) - one_changes - zero_changes
    min_nums = min(one_changes + two_changes*2,min_nums)
  print(min_nums)
  t-=1