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:
import sys

input = sys.stdin.readline

for _ in range(int(input())):
    n,k = list(map(int,input().split()))
    arr = list(map(int,input().split()))
    sums = dict()
    for i in range(len(arr)//2):
        if arr[i]+arr[n-1-i] not in sums:
            sums[arr[i]+arr[n-1-i]]=0
        sums[arr[i]+arr[n-1-i]]+=1
    mins = []
    maxs = []
    for i in range(len(arr)//2):
        mins.append(arr[i]+arr[n-1-i]-max(arr[i],arr[n-1-i])+1)
        maxs.append(arr[i]+arr[n-1-i]-min(arr[i],arr[n-1-i])+k)
    mins.sort()
    maxs.sort()
    minarr = []
    maxarr = []
    current = 0
    for i in range(2*k+1):
        while current<len(mins) and i==mins[current]:
            current+=1
        minarr.append(n//2-current)
    current = 0
    for i in range(2*k+1):
        while current<len(maxs) and i>maxs[current]:
            current+=1
        maxarr.append(current)
    ans = sys.maxsize
    for total in range(2,2*k+1):
        if total in sums:
            temp = n//2+minarr[total]+maxarr[total]-sums[total]
        else:
            temp = n//2+minarr[total]+maxarr[total]
        if temp<ans:
            ans=temp
    print(ans)