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:
# cook your dish here
import sys
import math
from collections import defaultdict
mod=1000000007
T=1
T=int(sys.stdin.readline())
for _ in range(T):
    n,k=map(int,input().split())
    l=list(map(int,input().split()))
    kk=(k<<1)
    a=[0]*(kk+5)
    d=defaultdict(int)
    p=[]
    nn=(n>>1)
    for i in range(nn):
        pp=(min(l[i],l[n-i-1]),max(l[i],l[n-i-1]))
        p.append(pp)
        a[pp[0]+1]+=1
        a[pp[1]+k+1]-=1
        d[pp[0]+pp[1]]+=1
    ans=n
    for i in range(1,len(a)):
        a[i]+=a[i-1]
    #print(*p)
    #print(*a)
    for i in range(2,kk+1):
        s=a[i]-d[i]+((nn-(a[i]))<<1)
        ans=min(ans,s)
    print(ans)