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 math
test = int(input())
i=1

while(i<=test):
	n=int(input())
	half = n//2
	mark = {}
	s1 = 1
	s2 = 2
	s3 = 5
	if(half%2!=0):
		print("NO")
	else:
		print("YES")
		count=0
		while(count<half):
			print(s2,end=" ")
			s2 = s2+2
			count+=1
		count=0
		c=True
		while(count<(half//2)):
			if(c):
				print(s1,end=" ")
				print(s3,end=" ")
				mark[s1]=1
				mark[s3]=1

				if(s1+2 not in mark):
					s1+=2
					s3+=6
				elif(s1+4 not in mark):
					s1+=4
					s3+=4
				elif(s1+6 not in mark):
					s1+=6
					s3+=2
			count+=1
		print()
	i+=1