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:
for test in range(int(input())):
    n, k = map(int, input().split())
    a = [*map(int, input().split())]
    breakdown = [(a[i], a[n - 1 - i]) for i in range(n//2) if not (a[i] > k and a[n - 1 - i] > k)]
    update = n -  2 * len(breakdown)
    score = [0 for value in range(2 * k + 2)]
    for pair in breakdown:
        a, b = pair
        if a <= k and b <= k:
            score[2] += 2
            score[min(a, b) + 1] -= 1
            score[max(a, b) + k + 1] += 1
            score[a + b] -= 1
            score[a + b + 1] += 1
        elif a >= k:
            score[2] += 2
            score[b + 1] -= 1
            score[b + k + 1] += 1
        elif b >= k:
            score[2] += 2
            score[a + 1] -= 1
            score[a + k + 1] += 1
    control = 0
    minimum = n
    for key in score[2 : 2 * k + 1]:
        control += key
        minimum = min(minimum, control)
    print(update + minimum)