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:
def foo(n, data, k):
    farr = [0] * (2 * k + 1)
    sarr = [0] * (2 * k + 2)
    i = 0
    while i < n // 2:
        farr[data[i] + data[size - i - 1]] += 1
        i += 1
    i = 0
    while i < n // 2:
        sarr[min(data[i], data[size - i - 1]) + 1] += 1
        sarr[max(data[i], data[size - i - 1]) + k + 1] -= 1
        i += 1
    i = 1
    while i < (2 * k + 1):
        sarr[i] += sarr[i - 1]
        i += 1
    i = 0
    minimum = int(2 * 10e5)
    while i <= k * 2:
        minimum = min(minimum, (sarr[i] - farr[i]) + 2 * (n // 2 - sarr[i]))
        i += 1

    print(minimum)

if __name__ == '__main__':
    test = int(input())
    while test:
        size, k = [int(x) for x in input().split()]
        data = [int(i) for i in input().split()]
        foo(size, data, k)
        test -= 1