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:
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