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:
t = int(input())
for i in range(t):
    a = []
    n = int(input())
    add = 0
    for _ in range(int(n / 2)):
        add += 2
        a.append(add)

    possible_nums = [1]
    for num in a:
        possible_nums.append(num + 1)

    total = []
    for j in range(len(possible_nums)):
        if len(total) < len(a) - 1:
            total.append(possible_nums[j])
        else:
            if len(a) != len(total) and (sum(a) - sum(total)) % 2 != 0 :
                total.append(sum(a) - sum(total))
            if sum(a) == sum(total) and len(a) == len(total):
                print("YES")
                result = []
                for k in a:
                    result.append(str(k))
                for k in total:
                    result.append(str(k))
                result = " ".join(result)
                print(result)
                break
            else:
                print("NO")
                break