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())

for x in range(t):
	n,k = map(int,input().split())
	arr = list(map(int, input().split()))

	arr_0 = [0 for i in range(2*k+1)]
	arr_1 = [0 for i in range(2*k+2)]

	for i in range(n//2):
		min_no = min(arr[i], arr[n-i-1])
		max_no = max(arr[i], arr[n-i-1])

		arr_0[min_no + max_no] += 1
		l_ind = min_no+1
		r_ind = max_no+k
		arr_1[l_ind] += 1
		arr_1[r_ind+1] -= 1

	for i in range(2,2*k+2):
		arr_1[i] += arr_1[i-1]
	ans = 10000000
	for i in range(2,2*k+1):
		cur_ans = (arr_1[i]-arr_0[i]) + 2*(n//2 - arr_1[i])
		if (cur_ans < ans):
			ans = cur_ans
	print(ans)