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:

#coding:utf-8



even = list()
odd = list()

t = input();
t = int(t)



for i in range(t) :
	n = input()
	n = int(n)
	if n % 2 == 0 :

		halfarray = int( n / 2 )  
		if halfarray % 2 == 0 :
			print("YES")
			a = 2
			for i in range(1 , halfarray+1) :
				even.append(a*i)

			
			ev = 0 
			od = 0	
			for j in range(halfarray) : 

				if j % 2 == 0 :
					aa = even[ev] - 1
					ev += 1
					odd.append(aa)
				else :
					kk = halfarray - ev
					aa = even[kk] + 1
					odd.append(aa)	

			for ev in even :
				print(ev , ' ' , end='')			
			for od in odd :
				print(od, ' ' , end='')
						
		else :
			print("NO")	

			
		odd.clear()
		even.clear()

	else :
		print("NO")