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 build_first_half_of_array() -> dict:
    first_half: list = [2]
    sum_of_first_half = 2
    for i in range(int(test_case / 2) - 1):
        element = first_half[-1] + 2
        first_half.append(element)
        sum_of_first_half += element

    return dict(array=first_half, sum=sum_of_first_half)


def build_second_half_of_array(sum_of_even_list: int) -> \
        list:
    second_half: list = [1]
    sum_of_second_half = 1
    for i in range(int(test_case / 2 - 2)):
        element = second_half[-1] + 2
        second_half.append(element)
        sum_of_second_half += element
    second_half.append(sum_of_even_list -
                       sum_of_second_half)
    return second_half


def merge_arrays(first_array, second_array) -> list:
    return first_array + second_array


def array_to_space_separated_string(array: list) -> str:
    return " ".join(map(str, array))


def valid_number_generator() -> str:
    even_number_dict = build_first_half_of_array()
    odd_number_list = build_second_half_of_array(
        even_number_dict["sum"])
    number_array = merge_arrays(
        even_number_dict["array"],
        odd_number_list
    )
    return array_to_space_separated_string(number_array)


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

if __name__ == "__main__":
    array_length: int = int(input())
    output: list = []

    while array_length > 0:
        test_case = int(input())
        # Invalid number
        if not_valid_number(test_case):
            output.append('NO')
        else:
            string_of_number = valid_number_generator()
            output.append("YES")
            output.append(string_of_number)
        array_length -= 1


    print_output(output)