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
input=lambda : stdin.readline().strip()
from math import ceil,sqrt,factorial,gcd
for _ in range(int(input())):
	n,k=map(int,input().split())
	l=list(map(int,input().split()))
	z=[0 for i in range(2*k+1)]
	z1=list(z)
	f=list(z)
	for i in range(ceil(n//2)):
		a=l[i]
		b=l[n-i-1]
		z[min(a,b)+1]+=1
		z1[max(a,b)+k]+=1
		f[a+b]+=1
	# print(z)
	# print(z1)
	# print(f)
	m=2*(n//2)
	if n%2==0:
		for i in range(2,len(z)):
			m-=z[i]
			z[i]=m-f[i]
			m+=z1[i]
	else:
		x=2*l[n//2]
		for i in range(2,len(z)):
			m-=z[i]
			z[i]=m-f[i]
			m+=z1[i]
			if x==i:
				pass
			elif i%2!=0:
				z[i]=float("infinity")
			else:
				z[i]+=1

	# print(z)
	print(min(z[2:]))
	# print(f)