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 bs(a):
    low = 0
    high = len(li) - 1
    while low <= high:
        if high - low < 5:
            for i in range(low, high+1):
                if li[i] >= a:
                    return i
            return 0
        mid = (low + high) // 2
        if li[mid] >= a:
            high = mid
        else:
            low = mid + 1


def bs2(a):
    low = 0
    high = len(l) - 1
    while low <= high:
        if high - low < 5:
            for i in range(low, high+1):
                if l[i] > a:
                    return len(l) - i
            return 0
        mid = (low + high) // 2
        if l[mid] > a:
            high = mid
        else:
            low = mid+1


t = int(input())
for _ in range(t):
    n, k = [int(x) for x in input().split()]
    s = list(map(int, input().split()))
    l = []
    li = []
    sum = []
    dict = {}
    for i in range(n // 2):
        l.append(min(s[i], s[n - 1 - i]))
        li.append(max(s[i], s[n - 1 - i]))
        if dict.get(s[i] + s[n - 1 - i]) is None:
            dict[s[i] + s[n - 1 - i]] = 0
        dict[s[i] + s[n - 1 - i]] += 1
    for x in dict.keys():
        sum.append((x, dict[x]))
    l.sort()
    li.sort()
    ans = n // 2
    for p in sum:
        x = 0
        y = 0
        if p[0] > k:
            x = p[0] - k
            y = k
            z = bs(x)
            ans = min(ans, (2 * z) + (n // 2) - z - p[1])
        else:
            x = 1
            y = p[0] - 1
            z = bs2(y)
            ans = min(ans, 2 * z + (n // 2) - z - p[1])
    print(ans)