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 os, sys, bisect, copy
from collections import defaultdict, Counter, deque
from functools import lru_cache   #use @lru_cache(None)
if os.path.exists('in.txt'): sys.stdin=open('in.txt','r')
if os.path.exists('out.txt'): sys.stdout=open('out.txt', 'w')
#
def input(): return sys.stdin.readline()
def mapi(arg=0): return map(int if arg==0 else str,input().split())
#------------------------------------------------------------------


for _ in range(int(input())):
    n,k = mapi()
    mp = defaultdict(int)
    a = list(mapi())
    x = 0
    res = float("inf")
    mx = [0]*(n//2)
    mn = [0]*(n//2)
    for i in range(n//2):
        mp[a[i]+a[n-i-1]]+=1
        mx[i] = max(a[i], a[n-i-1])+k
        mn[i] = min(a[i],a[n-i-1])+1
    mn.sort()
    mx.sort()
    for i in range(1,2*k+1):
        tmp = i
        #it1 = bisect.bisect_right(mx,tmp)-1
        #it2 = n//2-bisect.bisect_right(mn,tmp)+1
        #res = min(res,(n//2+it2+it1)-mp[tmp])
        a = bisect.bisect_right(mn,tmp)+1
        b = bisect.bisect_right(mx,tmp-1)+1
        res = min(res,2*(n//2)-a+b-mp[tmp])
    print(res)