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 make(vec, posi):
    vec[posi+1], vec[posi+2] = vec[posi+2], vec[posi+1]
    vec[posi], vec[posi+1] = vec[posi+1], vec[posi]
    return vec


def is_sorted(array):
    r = True
    for it in range(len(array)-1):
        if array[it] > array[it+1]:
            r = False
            break
    return r


for tc in range(int(input())):
    n = int(input())
    ar = list(map(int, input().split()))
    res = []
    for i in range(n):
        res.append([ar[i], i])
    res = sorted(res)
    #print(*res)
    for i in range(n):
        ar[res[i][1]] = i
    cnt = 0
    for i in range(n):
        for j in range(i+1, n):
            if ar[j] < ar[i]:
                cnt += 1
    #print("cnt&1 -> ",cnt&1)
    if cnt & 1:
        for i in range(n-1):
            if res[i][0] == res[i+1][0]:
                ar[res[i][1]], ar[res[i+1][1]] = ar[res[i+1][1]], ar[res[i][1]]
                break
    ans = []
    for i in range(n-2):
        #print("i ->",i)
        #print(*ans)
        pos = ar.index(min(ar[i:n]))
        while pos > i+1:
            ar = make(ar, pos - 2)
            ans.append(pos - 2)
            pos -= 2
        if pos != i:
            ar = make(ar, i)
            ar = make(ar, i)
            ans.append(i)
            ans.append(i)
            pos = i
    #print("last ans ",*ans)
    for i in range(3):
        #print("ans ",*ans)
        if is_sorted(ar):
            break
        ar = make(ar, n - 3)
        ans.append(n - 3)
    #print(*ans)
    #print(*ar)

    if not is_sorted(ar):
        print(-1)
    else:
        ans = [ans[i]+1 for i in range(len(ans))]
        print(len(ans))
        print(*ans)