Problem: You are given an array a consisting of n integers (it is guaranteed that n is even, i.e. divisible by 2). All a_i does not exceed some integer k.

Your task is to replace the minimum number of elements (replacement is the following operation: choose some index i from 1 to n and replace a_i with some integer in range [1; k]) to satisfy the following conditions:

  * after all replacements, all a_i are positive integers not greater than k; 
  * for all i from 1 to n/2 the following equation is true: a_i + a_{n - i + 1} = x, where x should be the same for all n/2 pairs of elements. 



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 first line of the test case contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 2 ⋅ 10^5) — the length of a and the maximum possible value of some a_i correspondingly. It is guratanteed that n is even (i.e. divisible by 2). The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ k), where a_i is the i-th element of a.

It is guaranteed that the sum of n (as well as the sum of k) over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5, ∑ k ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — the minimum number of elements you have to replace in a to satisfy the conditions from the problem statement.

Example

Input


4
4 2
1 2 1 2
4 3
1 2 2 1
8 7
6 1 1 7 6 3 4 6
6 6
5 2 6 1 3 4


Output


0
1
4
2

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)