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 PYTHON):

Solution:
from sys import stdin, stdout  
  
def main(): 
	N = int(stdin.readline()) 
	for tc in range(N):
		n = int(stdin.readline())
		odd = []
		even = []
		sumodd = 0
		sumeven = 0
		if (n / 2) % 2 != 0: 
			stdout.write(str('NO')+'\n')
			continue
		for x in range(n):
			if x % 2 == 0: 
				odd.append(x + 1)
				sumodd+=(x+1)
			else:
				even.append(x + 1)
				sumeven+=(x+1)
		diffe = (sumeven - sumodd) / 2
		for j in range(diffe):
			odd[len(odd) - 1 - j ]+=2
		stdout.write(str('YES')+'\n')

		ress = ' '.join(str(xx) for xx in even)
		ress2 = ' '.join(str(yy )for yy in odd)

		stdout.write(ress + ' ' +ress2+'\n')
if __name__ == "__main__": 
	main()