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_array(half_of_test_case: int) -> list:

    first_half: list = [2]
    for i in range(half_of_test_case - 1):
        first_half.append(first_half[-1] + 2)

    second_half: list = [1]
    for i in range(half_of_test_case - 2):
        second_half.append(second_half[-1] + 2)

    sum_of_even = half_of_test_case * (half_of_test_case
                                       + 1)
    sum_of_odd = ((half_of_test_case - 1) * (2 + (
        half_of_test_case - 2) * 2 )) / 2
    second_half.append(int(sum_of_even - sum_of_odd))
    return first_half + second_half


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


def valid_number_generator(n: int) -> str:

    number_array = build_array(int(n/2))
    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(
                test_case)
            output.append("YES")
            output.append(string_of_number)
        array_length -= 1


    print_output(output)