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:
MAX_VAL =400005
def countIntervals(arr, N):  
    minimum = 2*10**5+2
    maximum = 0
  
    # Frequency array to keep track of  
    # how many of the given intervals  
    # an element lies in  
    freq = [0] * (2*k+2)  
  
    for i in range(0, N): 
        li = arr[i][0]  
        freq[li] = freq[li] + 1
        ri = arr[i][1]  
        freq[ri + 1] = freq[ri + 1] - 1
  
        if li < minimum:  
            minimum = li  
          
        if ri > maximum: 
            maximum = ri  
              
    for i in range(minimum, maximum + 1):  
        freq[i] = freq[i] + freq[i - 1]  
  
    return freq 

for i in range(int(input())):
   n,k=map(int,input().split())
   l=list(map(int,input().split()))
   a=[]
   b=0
   c=0
   d=[]
   r=dict()
   for j in range(n//2):
       su=l[j]+l[n-1-j]
       a.append(su)
       b=1+min(l[j],l[n-1-j])
       c=k+max(l[j],l[n-1-j])
       if su in r:
           r[su]+=1
       else:
           r.update({su:1})
       d.append([b,c])
   a=list(set(a))
   u=len(d)
   tw=countIntervals(d,u)
   ans=999999999999999999999999999
   for j in range(len(a)):
       t=tw[a[j]]
       m=(n//2-t)*2+t-r[a[j]]
       ans=min(ans,m)
   print(min(n//2,ans))