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:
#x,y = map(int,input().split())
#from collections import Counter 
#arr = [int(i) for i in input().split()]
from collections import Counter
import math
mod = 10**9+7
for i in range(int(input())):
	n,k = map(int,input().split())
	arr = [int(i) for i in input().split()]
	d = {}
	for i in range(n//2):
		x = arr[i] + arr[n-i-1]
		if x not in d:
			d[x] = 1
		else:
			d[x] += 1
#	print(d)
	prefix = [0 for i in range(2*k+50)]
	for i in range(n//2):
		l = min(arr[i],arr[n-i-1]) + 1
		h = max(arr[i],arr[n-i-1]) + k
		prefix[l] += 1
		prefix[h+1] -= 1
#		print(i,prefix)
	s = 0
#	print(prefix)
	for i in range(2,2*k+1):
		s += prefix[i]
		prefix[i] = s
#	print(prefix)
	fans = 10**10
	for i in range(2,2*k+1):
		c0 = 0
		if i in d:
			c0 = d[i]
		c1 = prefix[i] - c0
		c2 = n//2 - c1 - c0
		total = c1+c2*2
		fans = min(fans,total)

	print(fans)