Problem: You are given a positive integer n, it is guaranteed that n is even (i.e. divisible by 2).

You want to construct the array a of length n such that: 

  * The first n/2 elements of a are even (divisible by 2); 
  * the second n/2 elements of a are odd (not divisible by 2); 
  * all elements of a are distinct and positive; 
  * the sum of the first half equals to the sum of the second half (∑_{i=1}^{n/2} a_i = ∑_{i=n/2 + 1}^{n} a_i). 



If there are multiple answers, you can print any. It is not guaranteed that the answer exists.

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 only line of the test case contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of the array. It is guaranteed that that n is even (i.e. divisible by 2).

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

Output

For each test case, print the answer — "NO" (without quotes), if there is no suitable answer for the given test case or "YES" in the first line and any suitable array a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) satisfying conditions from the problem statement on the second line.

Example

Input


5
2
4
6
8
10


Output


NO
YES
2 4 1 5
NO
YES
2 4 6 8 1 3 5 11
NO

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)