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:
from sys import stdin,stdout
# from collections import deque
# from heapq import heappush,heappop
Pi = lambda x: stdout.write(str(x) + '\n')
Ps = lambda x: stdout.write(str(x))
S = lambda x: x*(x+1) // 2
I = lambda x: 1+(2*x)
R = lambda:stdin.readline()
Ri = lambda x:map(int,x.split())
Rs = lambda x:map(str,x.split())
Rf = lambda x:map(float,x.split())
MaxN = 1<<60
def f(n):
	for i in range(2,int(n**0.5)+1):
		if n%i==0:return 1
	return 0

def main():
	test = int(R())
	
	for t in range(test):
		n = int(R())
		A = []
		if (n//2)%2==0:
			Pi('YES')
			for i in range(n//2):
				A.append((i+1)*2)
			B = []
			for i in range(n//2 - 1):
				B.append(i*2 + 1)
			B.append(sum(A)-sum(B))
			for i in A:
				Ps(str(i) + ' ')
			for i in B:
				Ps(str(i) + ' ')
			Ps('\n')
		else:
			Pi('NO')		
		
if __name__=='__main__':
    main()

# Esta mal el Problema?????
# pq = []
# heappush(pq,-1)
# heappush(pq,-3)
# heappush(pq,-2)
# while len(pq):
# 	Pi(-heappop(pq))