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:
import random, math
from copy import deepcopy as dc
from bisect import bisect_left, bisect_right


# Function to call the actual solution
def solution(n):
	li = []
	s = 0
	ele = 2
	for i in range((n//2)):
		s += ele
		li.append(ele)
		ele += 2
	s1 = 0
	ele = 1
	for i in range((n//2)-1):
		s1 += ele
		li.append(ele)
		ele += 2
	left = s - s1
	if left % 2 != 0:
		li.append(left)
		return li
	return []


# Function to take input
def input_test():
	for _ in range(int(input())):
		n = int(input())
		# a, b = map(int, input().strip().split(" "))
		# a, b, c = map(int, input().strip().split(" "))
		# li = list(map(int, input().strip().split(" ")))
		out = solution(n)
		if out:
			print("YES")
			print(*out)
		else:
			print("NO")


# Function to check test my code
def test():
	pass


input_test()
# test()