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 check_sum(n, k):
    sum_before_k = (k - 1) ** 2
    
    if n > sum_before_k:
        max_last_dig = (n-sum_before_k)
        if  max_last_dig % 2 == 1 and max_last_dig >= (2 * k - 1):
            result = []
            start = 1
            
            while sum_before_k:
                sum_before_k -= start
                result.append(start)
                start += 2
            
            return result + [max_last_dig]

t = int(input())
result = []

for _ in range(t):
    n = int(input())
    if (n / 2) % 2:
        result.append('NO')
    else:
        result.append('YES')
        
        array = []
        check = int(n/2)
        step = 1
        
        while check:
            array.append(2 * step)
            check -= 1
            step += 1
            
        sum_array = sum(array)
            
        array += check_sum(sum_array, int(n/2))
        result.append(array)
        
for res in result:
    if res == 'NO' or res == 'YES':
        print(res)
    else:
        print(' '.join(map(str, res)))