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:
'''
#		SHREYANS BHAVSAR	#
#       DDIT				#
#       @shreyans_9950		#
#       CF,CC,HE,HR,GFG		#
'''

# import math
# def shrey():
	# /*!@#$%^&*()-+=*/
	# s=list(input())
	# l=len(s)
	# ans=""
	# for i in range(l):
	# 	if(i==0 or i==l-1 or i%2!=0):
	# 		ans+=s[i]

	# print(ans)
	# n=int(input())
	# a=list(map(int,input().split()))
	# c=0
	# c1=0
	# for i in range(len(a)):
	# 	if(i%2==0 and  a[i]%2!=0):
	# 		c+=1
	# 	if(i%2!=0 and a[i]%2==0):
	# 		c1+=1
	# if(c!=c1):
	# 	print(-1)
	# else:
	# 	print(c)
	# a,b=input().split()
	# a=int(a)
	# b=int(b)
	# ans=(60-b)+((23-a)*60)
	# print(ans)
	# n,k=input().split()
	# n=int(n)
	# k=int(k)
	# print(n-max(0,n%k-k//2))
	# n,k=input().split()
	# n=int(n)
	# k=int(k)
	# for i in range(k):
	# 	if(n%10!=0):
	# 		n-=1
	# 	else:
	# 		n=n//10
	# print(n)

# T = input()
# T = int(T)
# for q in range(1,T+1):
	# /*shreyans bhavsar(DDIT)*/
	# shrey()
# n = int(input())
# str1 = input()
# lst1 = []
# for i in range(n-1):
#     lst1.append(str1[i:i+2])
 
# print (max(lst1,key=lst1.count))
# n,k=input().split()
# n=int(n)
# k=int(k)
# a=list(map(int,input().split()))

# a.sort()
# # print(*a)
# if(k==0):
# 	if(a[0]>1):
# 		print(1)
# 	else:
# 		print(-1)
# else:
# 	if(k==n or a[k]!=a[k-1]):
# 		print(a[k-1])
# 	else:
# 		print(-1)
# for i in range(int(input())):
# 	l,v,u,r=map(int,input().split())
# 	print(l//v-((r//v)-((u-1)//v)))
# for i in range(int(input())):
	# a,b,c=map(int,input().split())
	# ans=max(0,abs(a-b)+abs(a-c)+abs(b-c)-4)
	# print(ans)
# for i in range(int(input())):
# 	n=int(input())
# 	b=3
# 	j=3
# 	while n%b!=0:
# 		b=2**j-1
# 		j+=1
# 	print(n//b)
# for i in range(int(input())):
# 	n=int(input())
# 	if(n%3==0):
# 		print(n//3)
# 	else:
# 		b=3
# 		c=3
# 		while(n%b!=0):
# 			b=2**c-1
# 			c+=1
# 		print(n//b)
for q in range(int(input())):
	n=int(input())
	if((n//2)%2!=0):
		print("NO")
	else:
		s=0
		s1=0
		print("YES")
		ans=[]
		# ans.append(2)
		for i in range(0,n//2):
			c=2*(i+1)
			s+=c
			ans.append(c)
		for i in range(n//2,n-1):
			c=2*(i-n//2+1)-1
			s1+=c
			ans.append(c)
		d=s-s1
		ans.append(d)
		print(*ans)