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 _ in range(int(input())):
    n, k = map(int, input().split())
    data = list(map(int, input().split()))
  
    in_map = {}
    out_map = {}
    sum_map = {}
    
    points = set()
 
    for i in range(n // 2):
        min_value = min(data[i], data[n - i - 1])
        max_value = max(data[i], data[n - i - 1])

        lower_bound = min_value + 1
        upper_bound = max_value + k
        sum_value = min_value + max_value

        if lower_bound in in_map:
            in_map[lower_bound] += 1
        else:
            in_map[lower_bound] = 1

        if upper_bound in out_map:
            out_map[upper_bound] += 1
        else:
            out_map[upper_bound] = 1

        if sum_value in sum_map:
            sum_map[sum_value] += 1
        else:
            sum_map[sum_value] = 1

        points.add(lower_bound)
        points.add(upper_bound)
        points.add(sum_value)
  
    points = sorted(points)
 
    now_sum = 0
    result = n
  
    for i in points:
        in_count = 0
        if i in in_map:
            in_count = in_map[i]
        now_sum += in_count

        sum_count = 0
        if i in sum_map:
            sum_count = sum_map[i]

        now_total = n - (now_sum + sum_count)
        result = min(result, now_total)

        out_count = 0
        if i in out_map:
            out_count = out_map[i]
        now_sum -= out_count
    
    print(result)