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 PYTHON):

Solution:
def compute_array(element):
    output_array = []
    even_odd_numbers = element/2
    even_elements = [even_element*2 for even_element in range(1, even_odd_numbers + 1)]
    output_array.extend(even_elements)

    odd_elements = [odd_element*2 - 1 for odd_element in range(1, even_odd_numbers)]
    output_array.extend(odd_elements)

    output_array.append(sum(even_elements) - sum(odd_elements))

    return output_array


array_length = int(input())
input_array = []
for index in range(array_length):
    element = int(input())
    input_array.append(element)

for element in input_array:
    if (element / 2) % 2 != 0:
        print "NO"
        continue
    else:
        print "YES"
        output_array = compute_array(element)
        print " ".join(str(element) for element in output_array)