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:

def generateArray(n):
    half = n//2
    ans = []
    
    sum_ = 0
    even ,odd = 2,1
    for i in range(half):
        ans.append(even)
        sum_+=even
        even+=2
    
    
    for i in range(half-1):
        ans.append(odd)
        sum_-=odd
        odd+=2
    
    if sum_&1==1:
        ans.append(sum_)
        sum_=0
        
    # print(ans)
    
    return [ans, sum_==0]
        

if __name__=="__main__":
    t = int(input())

    for i in range(t):
        n = int(input())
        
        if (n//2)&1==1:
            print("NO")
        else:
            
            arr,poss = generateArray(n)
            
            if poss:
                print("YES")
                for idx,i in enumerate(arr):
                    if idx!=len(arr):
                        print(i, end=" ")
                    else:
                        print(i)
            else:
                print("NO")