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:
t = int(input())
numbers = []
final = []
total_even = 0
total_odd = 0

for i in range(t):
	num = input()
	numbers.append(int(num))


for j in numbers:
	final_string=''
	odd = 1
	if j == 2:
		print('NO')
	else:
		for i in range(1,(j//2)+1):
			final.append(i*2)
			total_even += (i*2)
		for i in range(1,(j//2)+1):

			if i == 1:
				final.append(odd)
				total_odd+=odd
			elif i == (j//2):
				# odd += 2
				# final.append(odd)
				# total_odd += odd
				if ((total_even-total_odd)%2 == 1):
					final.append(total_even-total_odd)
					print('YES')
					for f in final:
						final_string += str(f)
						final_string += ' '
					print(final_string)
				else:
					print('NO')


			else:
				odd+=2
				final.append(odd)
				total_odd += odd

		# print(final)
		final=[]
		total_even = 0
		total_odd = 0