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:
t = int(input())
def oco(l):
    d = {}
    for el in l:
        if el in d:
            d[el] += 1
        else:
            d[el] = 1
    return d
for test in range(t):
    n, k = [int(i) for i in input().split()]
    a = [int(i) for i in input().split()]
    psum = [a[i] + a[n-i-1] for i in range(len(a)//2)]
    pmax = [k+max(a[i], a[n-i-1]) for i in range(len(a)//2)]
    pmax.sort()
    pmin = [1+min(a[i], a[n-i-1]) for i in range(len(a)//2)]
    pmin.sort()
    di = oco(psum)
    itma = 0
    itmi = 0
    ans = [0 for i in range(2*k-1)]
    for i in range(len(ans)):
        while itma < len(pmax):
            if pmax[itma]>=i+2:
                break
            itma += 1
        while itmi < len(pmin):
            if pmin[itmi]>i+2:
                break
            itmi += 1
        ans[i] = n +itma- itmi
        if i+2 in di:
            ans[i]  -= di[i+2]
    print(min(ans))