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:
# ----------------------------
# Escape Sequences Characters
# \b => Back Space
# \newline => Escape New Line + \
# \\ => Escape Back Slash
# \' => Escape Single Quotes
# \" => Escape Double Quotes
# \n => Line Feed
# \r => Carriage Return
# \t => Horizontal Tab
# \xhh => Character Hex Value
# ----------------------------
# -- Strings Methods --
# strip() rstrip() lstrip()
# title() istitle() captilaze upper lower
# zfill
# split() rsp..
# ---------------------
# list it's look like array == []
# list is order & indexed & mutable & ununiqe
# tuple is order & indexed & unmutable & ununiqe == ()
# set is unorder & unindexed & unmutable & uniqe =={}
# -- Dictionary --
# [1] Dict Items Are Enclosed in Curly Braces
# [2] Dict Items Are Contains Key : Value
# [3] Dict Key Need To Be Immutable => (Number, String, Tuple) List Not Allowed
# [4] Dict Value Can Have Any Data Types
# [5] Dict Key Need To Be Unique
# [6] Dict Is Not Ordered You Access Its Element With Key
# ----------------------------
alph = "abcdefghijklmnopqrstuvwxyz"




# test your function

for _ in range(int(input())):
  n=int(input(""))
  if( (n//2)%2 == 1):
    print("NO")
  else:
    i=2;
    sum=0;
    a=[]
    for _ in range(n//2):
      sum=sum+i
      a.append(i)
      i+=2

    i=1; sum2=0
    for _ in range(n//2 - 1):
      a.append(i)
      sum2=sum2+i
      i=i+2
    a.append(sum-sum2)
    print("YES")
    for x in a:
      print(x, end=" ")
    print()