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 collections import deque
from collections import Counter
from itertools import permutations
import heapq

def counterExample():
    arr = [1, 3, 4, 1, 2, 1, 1, 3, 4, 3, 5, 1, 2, 5, 3, 4, 5]
    counter = Counter(arr)
    top_three = counter.most_common(3)
    print(top_three)

q = deque()

#For stack we have:
#q.append()
#q.pop()

#For queue we have:
#q.append()
#q.popleft()


#for heap we have:
#heapify(a list)
#heapq.heappush()
#heapq.heappop()
#heapq.nlargest(k, iterable, key = fun)
#heapq.nsmallest(k, iterable, key = fun)





def main():
    t = int(input())
    while t > 0:
        t -= 1
        n = int(input())
        if n % 4 != 0:
            print("NO")
        else:
            print("YES")
            a = [i * 2 for i in range(1, n // 2 + 1)]
            b = [i * 2 - 1 for i in range(1, n // 2 )]
            b.append(b[n // 2 - 2] + n // 2 + 2)
            a.extend(b)
            print(" ".join([str(i) for i in a]))





if __name__ == "__main__":
    main()