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
def BuubleSort(a):
	n = a//2
	stl  = (n-1)**2
	soe = (n+1)*n
	left = soe - stl
	le = [i for i in range(2 , 2*n+1 , 2)]
	lo = [i for i in range(1,2*n-1,2)]
	nl = []
	nl = le + lo
	nl.append(left)



	return nl






def main():
	
	n = int(input())
	
	#a,b = map(int , input().split())
	#l = list(map(int  , input().split()))
	for _ in range(n):
		#a,b = map(int , input().split())
		a = int(input())
		if (a//2)%2 == 0:
			ans= BuubleSort(a)
			print("YES")
			print(*ans)
		else:
			print("NO")
		
	


if __name__ == "__main__":
	main()