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
# from math import sqrt, floor, ceil
# from bisect import bisect
# from collections import deque, Counter
inp = sys.stdin.readline
read = lambda: list(map(int, inp().split()))

def a():
	ans = ""
	for _ in range(int(inp())):
		n = int(inp())
		s = "11"
		while n % int(s, 2) != 0:
			s += "1"
		ans += str(n // int(s, 2))+"\n"
	print(ans)

def b():
	ans = ""
	for _ in range(int(inp())):
		n = int(inp())
		if not (n//2)%2:
			ans += "YES\n"
			arr = [[], []]
			for i in range(1, n+2):
				if i != (n+2)//2:
					arr[i%2].append(str(i))
			# arr = [str(i) for i in range(1, n+2) if i != (n+2)//2]
			ans += (" ").join(arr[0]+arr[1])+"\n"
		else:
			ans += "NO\n"
	print(ans)





if __name__ == "__main__":
	# a()
	b()
	# c()
	# d()