Problem: You are given a positive integer n, it is guaranteed that n is even (i.e. divisible by 2).

You want to construct the array a of length n such that: 

  * The first n/2 elements of a are even (divisible by 2); 
  * the second n/2 elements of a are odd (not divisible by 2); 
  * all elements of a are distinct and positive; 
  * the sum of the first half equals to the sum of the second half (∑_{i=1}^{n/2} a_i = ∑_{i=n/2 + 1}^{n} a_i). 



If there are multiple answers, you can print any. It is not guaranteed that the answer exists.

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 only line of the test case contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of the array. It is guaranteed that that n is even (i.e. divisible by 2).

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — "NO" (without quotes), if there is no suitable answer for the given test case or "YES" in the first line and any suitable array a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) satisfying conditions from the problem statement on the second line.

Example

Input


5
2
4
6
8
10


Output


NO
YES
2 4 1 5
NO
YES
2 4 6 8 1 3 5 11
NO

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')