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:
from sys import stdin, stdout
from collections import Counter, defaultdict
#from itertools import permutations, combinations
raw_input = stdin.readline
pr = stdout.write


def in_num():
    return int(raw_input())


def in_arr():
    return map(int,raw_input().split())


def pr_num(n):
    stdout.write(str(n)+'\n')


def pr_arr(arr):
    pr(' '.join(map(str,arr))+'\n')

# fast read function for total integer input

def inp():
    # this function returns whole input of
    # space/line seperated integers
    # Use Ctrl+D to flush stdin.
    return stdin.read().split()

range = xrange # not for python 3.0+

# main code

for t in range(in_num()):
    n,k=in_arr()
    l=in_arr()
    dp=[0 for i in range(2*k+5)]
    for i in range(n/2):
        v1=l[i]
        v2=l[n-i-1]
        dp[min(v1,v2)+1]-=1
        dp[v1+v2]-=1
        dp[v1+v2+1]+=1
        dp[max(v1,v2)+k+1]+=1
    temp=n
    ans=temp
    for i in range(2,2*k+1):
        temp+=dp[i]
        ans=min(ans,temp)
    pr_num(ans)