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:
for t in range(int(input())):
	n, k = [int(j) for j in input().split()]
	l = [int(j) for j in input().split()]
	a = 0
	b = 0
	s = [0]*(2*k+1)
	t = [0]*(2*k+1)
	pre = [0]*(2*k)
	suf =  [0]*(2*k)
	for i in range(n//2):
		tmp = l[i]+l[n-i-1]
		s[tmp] += 1
		pre[min(l[i], l[n-i-1])]+=1
		suf[max(l[i], l[n-i-1])]+=1
	# pre = []*(2*k)
	# suf =  [s[n-1]]*(2*k)
	# print(suf)
	for i in range(1,len(pre)):
		pre[i] += pre[i-1]
		suf[i] += suf[i-1]
	# print(suf)
	# print(pre)
	# suf = suf[::-1]
	ans = n
	# print(s, suf, pre)
	for sum_ in range(1,2*k+1):
		tmp = suf[max(sum_-k-1, 0)]+n//2-s[sum_]+n//2-pre[max(sum_-1, 0)]
		# print(tmp, sum_, pre[max(sum_-2, 0)], suf[max(sum_-k-1, 0)], s[sum_])
		# print(tmp)
		ans = min(ans, tmp)
	print(ans)