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 bisect
def main():
    t = int(input())
    for _ in range(t):
        line = input().split()
        n, k = int(line[0]), int(line[1])
        nums = list(map(int, input().split()))
        dic = {}
        min_ = []
        max_ = []
        for i in range(n // 2):
            dic[nums[i] + nums[n - i - 1]] = dic.get(nums[i] + nums[n - i - 1], 0) + 1
            min_.append(min(nums[i], nums[n - i - 1]))
            max_.append(max(nums[i], nums[n - i - 1]))
        min_.sort()
        max_.sort()
        # pairs = sorted(dic.items())
        # m = len(pairs)
        # vals = [pairs[i][0] for i in range(m)]
        # nums = [pairs[i][1] for i in range(m)]
        # sums = [0 for _ in range(m)]
        # for i in range(m):
        #     if i == 0:
        #         sums[i] = nums[i]
        #     else:
        #         sums[i] = nums[i] + sums[i-1]
        m = len(min_)
        ans = m
        for key in dic:
            res = 0
            left = bisect.bisect_left(max_, key-k)
            # print(left)
            res += left * 2
            right = bisect.bisect_right(min_, key-1)
            # print(right)
            # print(dic[key])
            res += (m - right) * 2
            res += m - left - (m - right) - dic[key]
            ans = min(ans, res)
        print(ans)



if __name__ == "__main__":
    main()