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 solve(arr,s,k):
	hs = s // 2 
	bal = max(arr)
	unchanged1 = [0]*(bal+k+2)
	unchanged2 = [0]*(bal+k+2) 
	for i in range(hs):
		smax = max(arr[i],arr[s-1-i]) + k
		smin = min(arr[i],arr[s-1-i]) + 1 
		unchanged1[smin] += 1 
		unchanged1[smax+1] -= 1
		unchanged2[arr[i]+arr[s-1-i]] += 2 


	for i in range(1,bal+k+2) :
		unchanged1[i] += unchanged1[i-1]  
	for i in range(1,bal+k+1) :
		if(unchanged2[i] > 0) :
			unchanged1[i] += unchanged2[i] // 2
	mans = 0 
	for i in range(1,bal+k+1) :
		mans = max(mans,unchanged1[i],unchanged2[i]) 

	return s-mans





tc = int(input()) 

fun = solve
ans = ""

for ll in range(tc) :
	_,k = map(int,input().split()) 
	li  = [int(x) for x in input().split()] 
	fun(li,_,k)
	ans += "{}\n".format(fun(li,_,k))
print(ans)