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 as m
def f1():
	T=int(input())
	while(T!=0):
		T=T-1
		N=int(input())
		print(N/3)
		#val1=(N/x)+1
		#val2=m.log(val1)/m.log(2)
		#print(int(val2))

	#Arr=[int(i) for i in input().split()]


def f2():
	T=int(input())
	while(T!=0):
		T=T-1
		n=int(input())
		if((n//2)%2!=0):
			print("NO")
		else:
			E=[2*i for i in range(1,(n//2)+1)]
			O=[i for i in range(1,n-1,2)]
			se=sum(E)
			so=sum(O)
			O.append(se-so)
			print("YES")
			for i in E:
				print(i,end=" ")
			for i in O:
				print(i,end=" ")
			print()



	#Arr=[int(i) for i in input().split()]


if __name__ == '__main__':
	f2()