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:
# ANSHUL GAUTAM
# IIIT-D

from math import *
from copy import *					# ll = deepcopy(l)
from heapq import *					# heappush(hp,x)
from string import *				# alpha = ascii_lowercase
from random import *				# l.sort(key=lambda l1:l1[0]-l1[1]) => ex: sort on the basis difference
from bisect import *				# bisect_left(arr,x,start,end)  => start and end parameters are temporary
from sys import stdin				# bisect_left return leftmost position where x should be inserted to keep sorted
from sys import maxsize				# minn = -maxsize
from operator import *				# d = sorted(d.items(), key=itemgetter(1))
from itertools import *				# pre = [0] + list(accumulate(l))
from collections import Counter		# d = dict(Counter(l))
from collections import defaultdict # d = defaultdict(list)

'''

'''

def solve(n):
	ans = [0]*n
	if(n%4 != 0):
		print('NO')
	else:
		ii = 1
		s = 0
		for i in range(n//2):
			ans[i] = 2*ii
			ii += 1
			s += ans[i]
		ii = 1
		ss = 0
		for i in range(n//2,n-1):
			ans[i] = ii
			ii += 2
			ss += ans[i]
		ans[-1] = s-ss
		print('YES')
		print(*ans)

T = int(input())
for _ in range(T):
	N = int(stdin.readline())
	solve(N)