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:
from bisect import bisect, bisect_left, bisect_right


def solve():
    n, k = map(int, input().split())
    ar = list(map(int, input().split()))

    ocr = {}
    mpv = [None] * (n // 2)
    spv = [None] * (n // 2)

    for i in range(n // 2):
        x = ar[i] + ar[n - i - 1]
        mpx = max(ar[i], ar[n - i - 1]) + k
        spx = min(ar[i], ar[n - i - 1]) + 1

        spv[i] = spx
        mpv[i] = mpx

        if x in ocr:
            ocr[x] += 1
        else:
            ocr[x] = 1

    mpv.sort()
    spv.sort()

    items = [(v, k) for k, v in ocr.items()]
    items.sort()
    items.reverse()

    best = n // 2

    for ocr, x in items:
        over = bisect_left(mpv, x, 0, len(mpv))
        under = n // 2 - bisect_right(spv, x, 0, len(spv))

        cur = n // 2 - ocr + over + under

        if cur < best:
            best = cur

    print(best)


t = int(input())

for _ in range(t):
    solve()

# solve()