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:
t=int(input())
inf=float("INF")
def u(i,v):
	i+=2*k
	tr[i]+=v
	while i>1:
		i>>=1
		tr[i]=tr[i<<1]+tr[i<<1|1]
def q(i):
	l=2*k+1
	r=i+2*k+1
	res=0
	while l<r:
		if l&1:
			res+=tr[l]
			l+=1
		if r&1:
			r-=1
			res+=tr[r]
		l>>=1
		r>>=1
	return(res)

for _ in range(t):
	n,k=map(int,input().split())
	aa=list(map(int,input().split()))
	
	tr=[0 for i in range(4*(2*k+5))]
	for i in range(n//2):
		x=aa[i]+aa[n-1-i]
		a=1+min(aa[i],aa[n-1-i])
		b=k+max(aa[i],aa[n-1-i])
		if a<x and x<b:
			u(1,2)
			u(a-1,-1)
			u(x-1,-1)
			u(x,1)
			u(b,1)
		elif x==a and x==b:
			u(1,2)
			u(x-1,-2)
			u(x,2)
		elif x==a:
			u(1,2)
			u(x-1,-2)
			u(x,1)
			u(b,1)
		elif x==b:
			u(1,2)
			u(a-1,-1)
			u(x-1,-1)
			u(x,2)

	ans=n
	for i in range(1,2*k):
		ans=min(ans,q(i))
		
	print(ans)