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=[int(x) for x in input().split()]
    arr=[int(x) for x in input().split()]

    # Now the sum can range from 2 to 2*k
    '''
    Since the sum can vary from 2 to 2*k we create a prefix array and each element in the array is a value of x that give the number of pairs that can give that x in one change
    '''

    count=[0 for i in range(2*k+1)]
    pref=[0 for i in range(2*k+2)]
    for i in range(len(arr)//2):
        summ=arr[i]+arr[-(i+1)]
        count[summ]+=1
        minval=1+min(arr[i],arr[-(i+1)])
        maxval=k+max(arr[i],arr[-(i+1)])
        pref[minval]+=1
        pref[maxval+1]-=1
    
    # print(count)


    for i in range(1,len(pref)):
        pref[i]+=pref[i-1]

    # print(pref)
    ans=n
    for i in range(2,2*k+1):
        #Assume the current x is i and calculate the total number of changes required
        changes=pref[i] - count[i]+(n//2 - pref[i])*2
        ans=min(ans,changes)

    print(ans)