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:
test=int(input())
b=[False for _ in range(200005)]
c=[False for _ in range(200005)]
d=[False for _ in range(400005)]
for t in range(0,test):
  n,k=map(int,input().split())
  a=list(map(int,input().split()))
  res=2000000000
  for i in range(0,k*2+1):
    d[i]=0
  for i in range(0,k+2):
    b[i]=0
    c[i]=0
  for i in range(0,n//2):
    d[a[n-i-1]+a[i]]=d[a[n-i-1]+a[i]]+1
    b[max(a[n-i-1],a[i])]=b[max(a[n-i-1],a[i])]+1
    c[min(a[n-i-1],a[i])]=c[min(a[n-i-1],a[i])]+1
  for i in range(1,k+2):
    b[i]=b[i-1]+b[i]
  for i in range(k,-1,-1):
    c[i]=c[1+i]+c[i]
  for i in range(0,k*2+1):
    x=n//2-d[i]
    if(k>=i):
      x=x+c[i]
    else:
      x=x+b[i-1-k]
    res=min(x,res)
  print(res)