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:
for nt in range(int(input())):
	n,k=map(int,input().split())
	l=list(map(int,input().split()))
	s=[]
	d={}
	for i in range(n//2):
		a=l[i]+l[n-i-1]
		s.append((a,i))
		if a in d:
			d[a]+=1
		else:
			d[a]=1
	s.sort()
	if s[0][0]==s[-1][0]:
		print (0)
		continue
	r=[]
	start={}
	end={}
	for i in range(n//2):
		m1=max(l[i],l[n-i-1])
		m2=min(l[i],l[n-i-1])
		if m2+1 in start:
			start[m2+1]+=1
		else:
			start[m2+1]=1
		if m1+k in end:
			end[m1+k]+=1
		else:
			end[m1+k]=1
		# r.append((m2+1,m1+k))

	if 2 not in start:
		start[2]=0
	if 2 not in end:
		end[2]=0
	for i in range(3,2*k+1):
		if i not in start:
			start[i]=start[i-1]
		else:
			start[i]+=start[i-1]
		if i not in end:
			end[i]=end[i-1]
		else:
			end[i]+=end[i-1]
	ans=0
	# print (start,end)
	if 2 in d:
		ans=2*(n//2-start[2])-d[2]+start[2]
	else:
		ans=2*(n//2-start[2])+start[2]
	for i in range(3,2*k+1):
		# print (i,n//2-start[i]+end[i-1])
		if i in d:
			ans=min(ans,2*(n//2-start[i]+end[i-1])-d[i]+start[i]-end[i-1])
		else:
			ans=min(ans,2*(n//2-start[i]+end[i-1])+start[i]-end[i-1])
	print (ans)