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:
def binsearch(a, x):
	left = 0
	right = len(a)
	while right > left + 1:
		mid = (left + right) // 2
		#print('mid = ' + str(mid))
		if a[mid][0] > x:
			right = mid
		else:
			left = mid
	return left

t = int(input())
for _ in range(t):
	n, k = tuple(map(int, input().split()))
	a = list(map(int, input().split()))
	count = {}
	ranges = {}
	for i in range(n // 2):
		s = a[i]+a[n-i-1]
		if s in count:
			count[s] += 1
		else:
			count[s] = 1
		left = min(a[i],a[n-i-1])+1
		right = max(a[i],a[n-i-1])+k+1
		if left in ranges:
			ranges[left] += 1
		else:
			ranges[left] = 1
		if right in ranges:
			ranges[right] -= 1
		else:
			ranges[right] = -1
	runningsum = 0
	partials = []
	for key in sorted(ranges.keys()):
		runningsum += ranges[key]
		partials.append((key, runningsum))
	assert(runningsum == 0)
	#print(partials)
	res = n // 2
	for k, v in count.items():
		#print('searching ' + str(k))
		idx = binsearch(partials, k)
		res = min(res, n - partials[idx][1] - v)
	print(res)