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:
for _ in range(int(input())):
    n, k = map(int, input().split())
    data = list(map(int, input().split()))
  
    in_map = {}
    out_map = {}
    sum_map = {}
    
    points = set()
 
    for i in range(n // 2):
        min_value = min(data[i], data[n - i - 1])
        max_value = max(data[i], data[n - i - 1])

        lower_bound = min_value + 1
        upper_bound = max_value + k
        sum_value = min_value + max_value

        if lower_bound in in_map:
            in_map[lower_bound] += 1
        else:
            in_map[lower_bound] = 1

        if upper_bound in out_map:
            out_map[upper_bound] += 1
        else:
            out_map[upper_bound] = 1

        if sum_value in sum_map:
            sum_map[sum_value] += 1
        else:
            sum_map[sum_value] = 1

        points.add(lower_bound)
        points.add(upper_bound)
        points.add(sum_value)
  
    points = sorted(points)
 
    now_sum = 0
    result = n
  
    for i in points:
        in_count = 0
        if i in in_map:
            in_count = in_map[i]
        now_sum += in_count

        sum_count = 0
        if i in sum_map:
            sum_count = sum_map[i]

        now_total = n - (now_sum + sum_count)
        result = min(result, now_total)

        out_count = 0
        if i in out_map:
            out_count = out_map[i]
        now_sum -= out_count
    
    print(result)