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

def help():

	n,k=map(int,stdin.readline().split(" "))
	arr=list(map(int,stdin.readline().split(" ")))

	readucearr=[0]*(2*k+5)
	donearr=[0]*(2*k+5)

	for i in range(n//2):
		a1=arr[i]
		a2=arr[n-i-1]

		a1,a2=min(a1,a2),max(a1,a2)

		readucearr[a1+1]+=1
		readucearr[a2+k+1]-=1

		donearr[a1+a2]+=1

	ans=10000000
	sumyet=0
	for i in range(0,2*k+5):
		sumyet+=readucearr[i]
		if(i>=2 and i<=2*k):
			posians=(n//2-sumyet)*2+(sumyet- donearr[i])
			ans=min(ans,posians)
	print(ans)

for i in range(int(stdin.readline())):
	help()


# def help(ii):
# 	# stri=stdin.readline().strip("\n")
	
# #	row,col,r1,c1,r2,c2=map(int,stdin.readline().split(" "))

# 	arr=[[0]*row for i in range(col)]



# #	print("Case #"+str(ii+1)+":",east,south)



# for i in range(int(stdin.readline())):
# 	help(i)

# row,col=map(int,stdin.readline().split(" "))

# def func(row,col):
# 	arr=[[0]*(col) for i in range(row)]

# 	arr[0][0]=1

# 	for i in range(row):
# 		for j in range(col):
# 			if(i+1==row and j+1==col):
# 				continue
# 			elif(i+1==row):
# 				arr[i][j+1]+=arr[i][j]
# 			elif(j+1==col):
# 				arr[i+1][j]+=arr[i][j]
# 			else:
# 				arr[i+1][j]+=arr[i][j]/2
# 				arr[i][j+1]+=arr[i][j]/2

# 	for i in range(row):
# 		print(*arr[i],sep="\t\t")

# func(8,8)