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:
# TODO need to read editorial for this one

def solve(a, k):
    half = len(a) // 2

    buckets = [0 for x in range(2*(k+2))]
    for i in range(half):
        min_value = min(a[i], a[~i])
        max_value = max(a[i], a[~i])
        buckets[1] += 2
        buckets[min_value + 1] -= 1
        buckets[min_value + max_value] -= 1
        buckets[min_value + max_value + 1] += 1
        buckets[max_value + k + 1] += 1

    curr = 0
    result = 99999999999999999999
    for i in buckets[1:]:
        curr += i
        result = min(result, curr)

    return result

if __name__ == "__main__":
    for i in range(int(input())):
        n, k = map(int, input().split())
        a = [int(x) for x in input().split()]
        print(solve(a, k))