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 max_overlap(start, end):
    n = len(start)

    start.sort()
    end.sort()
    # print('Start', start)
    # print('End', end)

    inter = 1
    max_inter = 1
    # time = start[0]
    i = 1
    j = 0
    while i < n and j < n:
        if start[i] <= end[j]:
            inter += 1
            if inter > max_inter:
                max_inter = inter
                # time = start[i]
            i += 1
        else:
            inter -= 1
            j += 1

    # print('Time', time)
    return max_inter


t = int(input())
for _ in range(t):
    n, k = map(int, input().split())
    a = list(map(int, input().split()))

    total = 0
    start = []
    end = []
    for i in range(n//2):
        small, big = a[i], a[n-i-1]
        if small > big:
            small, big = big, small

        mini = small + 1
        maxi = big + k

        start.append(mini)
        end.append(maxi+0.1)

        start.append(big+small)
        end.append(big+small+0.1)

    overlap = max_overlap(start, end)
    # print('Overlap', overlap)
    print(n - overlap)
    # print('')