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:
tests = int(input())
 
for test in range(tests):
	n = int(input())
	
	size = int(n/2)
	even_arr = [2]
	even_sum = 2
	for each in range(1, size):
		value = even_arr[each-1] + 2
		even_arr.append(value)
		even_sum = even_sum + value

	odd_arr = [1]
	odd_sum = 1
	for each in range(1, size-1):
		value = odd_arr[each-1] + 2
		odd_arr.append(value)
		odd_sum = odd_sum + value
 
	last_num = even_sum - odd_sum
	if last_num in odd_arr or last_num % 2 == 0:
		print('NO')
	else:
		odd_arr.append(last_num)
		arr = even_arr + odd_arr
		
		result = ' '.join([str(elem) for elem in arr]) 
		print('YES')
		print(result)