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 
try:
    sys.stdin = open('input.txt', 'r') 
    sys.stdout = open('output.txt', 'w')
except:
    pass

input = sys.stdin.readline
for _ in range(int(input())):
	n,k = map(int,input().split())
	l = list(map(int,input().split()))
	count = {}

	d = {}
	for i in range(n//2):
		summ = l[i]+l[n-i-1]
		if d.get(summ):
			d[summ] += 1
		else:
			d[summ] = 1
		if count.get(summ):
			count[summ] += 1
		else:
			count[summ] = 1

	pref = [0]*(2*k+2)
	# print(pref)

	for i in range(n//2):
		slo = min(l[i]+1,l[n-i-1]+1)
		elo = max(l[i]+k,l[n-i-1]+k)
		# print(slo,elo+1)
		pref[slo] += 1
		pref[elo+1] -= 1
		# print(pref[slo],pref[elo+1])

	for i in range(1,len(pref)):
		pref[i] += pref[i-1]
	# print(pref)
	ans = n//2
	for i in d:
		ans = min(ans,n-d[i]-pref[i])
	sys.stdout.write((str(ans)+'\n'))