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
import math
'''import io, os
import bisect
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline'''
power=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
       27,28,29,30,31,32]
t=int(input())
for ijk in range(t):
  n,k=map(int,input().split())
  arr=[int(i) for i in input().split()]
  a1,a2=[0]*(2*(k)+2),[0]*(2*(k)+2)
  for i in range(len(arr)//2):
     xy=min(arr[i],arr[-i-1])
     yx=max(arr[i],arr[-i-1])
     a1[xy]+=1
     if xy!=arr[i]+arr[-i-1]-1:
        a1[arr[i]+arr[-i-1]-1]+=1
     a2[yx+k+1]+=1
     if yx!=arr[i]+arr[-i-1]+1:
        a2[arr[i]+arr[-i-1]+1]+=1
  #print(a1,a2,xy+yx)
  pref,suff=[0],[0]
  pref[0]=a1[-1]
  suff[0]=a2[0]
  for i in range(1,len(a1)):
     pref.append(a1[-i-1]+pref[-1])
     suff.append(a2[i]+suff[-1])
  pref.reverse()
  mina=math.inf
  #print(pref,suff)
  for i in range(1,(2*k+1)):
     #print(i,k,2*k+1)
     mina=min(mina,pref[i]+suff[i])
  sys.stdout.write(str(mina)+'\n')