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:
import collections 
t = int(input())

for i in range(t):

	n,k = tuple(map(int,input().split()))
	nums = list(map(int,input().split()))
	temp = n //2

	add = collections.defaultdict(int)

	for j in range(temp):
		add[nums[j]+nums[n-1-j]] += 1

	prefix = [0]*((2*k)+2)

	for j in range(temp):
		l1 = nums[j]
		l2 = nums[n-j-1]

		r = max(l1,l2) + k + 1

		prefix[min(l1,l2)+1] += 1
		prefix[r] -= 1
	for j in range(1,(2*k)+2):
		prefix[j] = prefix[j]+prefix[j-1]
	ans = float("inf")

	for j in range((2*k)+2):
		cnt0 = add[j]
		cnt1 = prefix[j]-cnt0

		cnt2 = temp - cnt0 - cnt1

		ans = min(ans,cnt1+(cnt2*2))

	print(ans)