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:
import sys

#list(map(int, sys.sdtin.readline().split()))
#map(int, sys.sdtin.readline().split())

t = int(sys.stdin.readline())
for _ in range(t):
	n, k = map(int, sys.stdin.readline().split())
	array = list(map(int, sys.stdin.readline().split()))
	out = 10**9
	maxs = list()
	mins = list()
	somme = [0]*(2*k+1)
	maxi = 0
	for i in range(n//2):
		s = array[i]+array[n-i-1]
		somme[s] += 1
		maxs.append(s-min(array[i], array[n-i-1])+k)
		mins.append(s-max(array[i],array[n-i-1])+1)
	maxs.sort()
	mins.sort()
	imax = 0
	imin = 0
	lenmin = len(mins)
	lenmax = len(maxs)
	for i in range(2, 2*k+1):
		while imax != lenmax and i > maxs[imax] :
			imax += 1
		while imin != lenmin and i >= mins[imin]:
			imin += 1
		double = (lenmin-imin) + imax
		total = ((n//2)-(somme[i])-double) + 2*double
		out = min(out, total)
		#print(total, double, somme[i])
	print(out)