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:
cnt = [0] * int(4e5 + 5)
f = [0] * int(4e5 + 5)
q = int(input())


while(q > 0):
	q -= 1
	n , k = map(int , input().split())
	a = list(map(int , input().split()))
	#init
	for i in range(n // 2):
		j = n - 1 - i
		if(a[i] > a[j]):
				temp = a[i]
				a[i] = a[j]
				a[j] = temp
		cnt[max(a[i] + 1 , 2)] -= 1
		cnt[min(a[j] + k + 1 , 2 * k + 1)] += 1
		f[a[i] + a[j]] += 1
	#solve
	temp = n
	res = int(2e9)
	for i in range(2 , 2 * k + 1):
		temp += cnt[i]
		res = min(res , temp - f[i])
	
	#reset
	for i in range(n // 2):
		j = n - 1 - i
		if(a[i] > a[j]):
			swap(a[i] , a[j])
		cnt[max(a[i] + 1 , 2)] = 0
		cnt[min(a[j] + k + 1 , 2 * k + 1)] = 0
		f[a[i] + a[j]] = 0


	print(res)