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:
from sys import stdin,stdout
# input = stdin.readline
from math import *
# print = stdout.write

for __ in range(int(input())):
	# ttt=False
	n,m=map(int,input().split())
	ar=list(map(int,input().split()))
	# if(__==0 and n==8 and m==8):
	# 	ttt=True
	r1={}
	r2={}
	h=[0]*(m+m+1)
	for i in range(n//2):
		x=ar[i]
		y=ar[-(i+1)]
		h[x+y]-=1
		a=1+min(x,y)
		b=m+max(x,y)
		if(r1.get(a)==None):
			r1[a]=1
		else:
			r1[a]+=1

		if(r2.get(b)==None):
			r2[b]=1
		else:
			r2[b]+=1
	# print(h)
	# print(r1)
	# print(r2)
	ans=n
	rslt=n
	for i in range(2,m+m+1):
		if(r1.get(i)!=None):
			ans-=r1[i]
		rslt=min(ans+h[i],rslt)
		if(r2.get(i)!=None):
			ans+=r2[i]
		# print(ans+h[i],i)
	print(rslt)