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 not_valid_number(number: int) -> bool:
    return not ((number / 2) % 2 == 0)


def get_output_number(input_number :int) -> str:
    even_set :list= [2]
    odd_set :list= [1]
    for i in range(3, (input_number), 2):
        even_set.append(i+1)

        odd_set.append(i)

    digit_number = int (input_number / 2)
    odd_set[-1] = (digit_number * (
            digit_number + 1)) + odd_set[-1] - sum(odd_set)

    return " ".join(map(str, (even_set + odd_set)))


def print_output(array: list):
    for i in array:
        print(i)

if __name__ == "__main__":
    result = []
    number_of_input: int = int(input())
    while number_of_input > 0:
        input_number = int(input())
        if not_valid_number(input_number):
            result.append('NO')

        else:
            result.append('YES')
            result.append(get_output_number(
                int(input_number)))

        number_of_input -= 1

    print_output(result)