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 PYTHON):

Solution:
import atexit, io, sys 

  
# A stream implementation using an in-memory bytes  
# buffer. It inherits BufferedIOBase. 

buffer = io.BytesIO() 

sys.stdout = buffer

  
# print via here 

@atexit.register 

def write(): 

    sys.__stdout__.write(buffer.getvalue()) 
for _ in range(input()):
    n,k=map(int,raw_input().split())
    a=map(int,raw_input().split())
    p=[]
    f=[0 for j in range(2*k+1)]
    for j in range(n/2):
        f[a[j]+a[n-j-1]]+=1
        p.append([a[j]+a[n-j-1]-
max(a[j],a[n-j-1])+1,a[j]+a[n-j-1]+
k-min(a[j],a[n-j-1])])
    p=sorted(p)
    q=[]
    for i in p:
       q.append([i[1],i[0]])
    q=sorted(q)
    po=0;qo=0
    to=0;tc=0
    m=float('inf')
    
   
    for j in range(2,2*k+1):
        
        while po<len(p) and p[po][0]<=j:
            to+=1
            po+=1
        while qo< len(q) and q[qo][0]<j:
            tc+=1
            qo+=1
        
        s=2*(n/2-(to-tc))+to-tc-f[j]
        
        if s<m:
            m=s;
    print m