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 f(number):
    answer_list = []
    sum = 0
    x = 2
    for i in range(0, number // 2):
        answer_list.append(x)
        sum += x
        x += 2
    y = 1
    sum_2 = 0
    for i in range(0, number // 2):
        if i == number // 2 - 1:
            z = sum - sum_2
            answer_list.append(z)
        else:
            answer_list.append(y)
            sum_2 += y
            y += 2
    answer_list = list(map(str, answer_list))
    answer_string = ' '.join(answer_list)
    return answer_string

first_number = int(input())
list_of_answer = [] 
for i in range(0, first_number):
    number = int(input())
    taqsim_b_2 = number / 2
    if taqsim_b_2 % 2 != 0:
        list_of_answer.append('NO')
    else:
        list_of_answer.append('YES')
        list_of_answer.append(f(number))
for i in list_of_answer:
    print(i)