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())
for _ in range(t):
    n, k = list(map(int, input().split()))
    a = list(map(int, input().split()))
    ma = max(a[0], a[-1])
    mi = min(a[0], a[-1])
    start = a[0] + a[-1] - (ma - 1)
    end = a[0] + a[-1] + (k - mi)
    s=[]
    e=[]
    s.append(start)
    e.append(end)
    events = [0 for _ in range(2*k+2)]
    events[start]+=1
    events[end+1]-=1
    for i in range(1, len(a) // 2):
        ma = max(a[i], a[n - i - 1])
        mi = min(a[i], a[n - i - 1])
        s.append(a[i] + a[n - i - 1] - (ma - 1))
        e.append(a[i] + a[n - i - 1] + (k - mi))
        events[s[-1]] += 1
        events[e[-1]+1] -= 1
    # print(s,e,events)
    sums={}
    for i in range(0,len(a)//2):
        if a[i]+a[n-i-1] not in sums:
            sums[a[i]+a[n-i-1]]=0
        sums[a[i]+a[n-i-1]]+=1
    prefix=[0 for _ in range(2*k+1)]
    minimum=1e10

    for i in range(2,2*k+1):
        prefix[i]=prefix[i-1]+events[i]

        minimum=min(minimum,(n//2-prefix[i])*2+(prefix[i]-sums.get(i,0)))
    # print(prefix, sums)
    print(minimum)