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 PYTHON):

Solution:
def binSearch(lst, x, l, r):#return the highest m s.t. lst[m] <= x (if x in array, rightmost instance)
	while l+1 < r:
		m = (l+r)//2
		# print l, m, r
		q = lst[m]
		if q <= x:
			l = m
		else:
			r = m
	return l
	
def binSearchR(lst, x, l, r):#return the lowest m s.t. lst[m] >= x (if x in array, leftmost instance)
	while l+1 < r:
		m = (l+r)//2
		q = lst[m]
		if q < x:
			l = m
		else:
			r = m
	return r
	
# lst = [4, 5, 6, 7]
# print binSearch(lst, 1, 0, 3)

I=lambda: map(int, raw_input().split())
t = input()
for _ in xrange(t):
	n,k = I()
	q = n//2
	a = I()
	ms = []
	Ms = []
	d = {}
	for i in xrange(q):
		w1 = a[i]
		w2 = a[n-1-i]
		s = w1+w2
		if s not in d:
			d[s] = 0
		d[s] += 1
		Ms.append(max(w1, w2))
		ms.append(min(w1, w2))
	Ms.sort()
	ms.sort()
	rm = q
	if k+1 in d:
		rm -= d[k+1]
	for x in d.keys():
		if x > k+1:
			y = x-k
			if Ms[0] >= y:
				i = 0
			elif Ms[-1] < y:
				i = q
			else:
				i = binSearchR(Ms, y, 0, q-1)
			newRm = 2*i + (q-i) - d[x]
			rm = min(rm, newRm)
		elif x < k+1:
			y = x-1
			if ms[0] > y:
				i = q
			elif ms[-1] <= y:
				i = 0
			else:
				i = binSearch(ms, y, 0, q-1)
				i += 1
				i = q-i
			newRm = 2*i + (q-i) - d[x]
			rm = min(rm, newRm)
	print rm