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 PYTHON):

Solution:
import atexit, io, sys 

  
# A stream implementation using an in-memory bytes  
# buffer. It inherits BufferedIOBase. 

buffer = io.BytesIO() 

sys.stdout = buffer

  
# print via here 

@atexit.register 

def write(): 

    sys.__stdout__.write(buffer.getvalue()) 
for _ in range(input()):
    n,k=map(int,raw_input().split())
    a=map(int,raw_input().split())
    p=[]
    f=[0 for j in range(2*k+1)]
    for j in range(n/2):
        f[a[j]+a[n-j-1]]+=1
        p.append([a[j]+a[n-j-1]-
max(a[j],a[n-j-1])+1,a[j]+a[n-j-1]+
k-min(a[j],a[n-j-1])])
    p=sorted(p)
    q=[]
    for i in p:
       q.append([i[1],i[0]])
    q=sorted(q)
    po=0;qo=0
    to=0;tc=0
    m=float('inf')
    
   
    for j in range(2,2*k+1):
        
        while po<len(p) and p[po][0]<=j:
            to+=1
            po+=1
        while qo< len(q) and q[qo][0]<j:
            tc+=1
            qo+=1
        
        s=2*(n/2-(to-tc))+to-tc-f[j]
        
        if s<m:
            m=s;
    print m