Problem: You are given an array a consisting of n integers (it is guaranteed that n is even, i.e. divisible by 2). All a_i does not exceed some integer k.

Your task is to replace the minimum number of elements (replacement is the following operation: choose some index i from 1 to n and replace a_i with some integer in range [1; k]) to satisfy the following conditions:

  * after all replacements, all a_i are positive integers not greater than k; 
  * for all i from 1 to n/2 the following equation is true: a_i + a_{n - i + 1} = x, where x should be the same for all n/2 pairs of elements. 



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 first line of the test case contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 2 ⋅ 10^5) — the length of a and the maximum possible value of some a_i correspondingly. It is guratanteed that n is even (i.e. divisible by 2). The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ k), where a_i is the i-th element of a.

It is guaranteed that the sum of n (as well as the sum of k) over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5, ∑ k ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — the minimum number of elements you have to replace in a to satisfy the conditions from the problem statement.

Example

Input


4
4 2
1 2 1 2
4 3
1 2 2 1
8 7
6 1 1 7 6 3 4 6
6 6
5 2 6 1 3 4


Output


0
1
4
2

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()