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:
for _ in range(input()):
	n,k=map(int,raw_input().split())
	l=map(int,raw_input().split())
	f=[0]*(2*k+3)
	ans=1e10
	d={}
	for i in range(n/2):
	    try:
	        d[l[i]+l[n-i-1]]+=1
	    except KeyError:
	        d[l[i]+l[n-i-1]]=1
	    a,b=min(l[i],l[n-i-1])+1,max(l[i],l[n-i-1])+k
	    f[a]+=1
	    f[b+1]-=1
	p=0
	for i in range(1,len(f)):
	    if f[i]==0:
	        f[i]=f[i-1]
	    else:
	        f[i]+=f[i-1]
	for x in range(2,2*k +1):
	    try:
	        ans=min(ans,f[x]+ n-(2*f[x])-d[x])
	    except KeyError:
	        ans=min(ans,f[x]+ n-(2*f[x]))
	print ans