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 make_first(n):
    k = 2
    i = 0
    first = []
    while i < n:
        first.append(k)
        k += 2
        i += 1
    return first

def make_second(n,sum_first):
    k = 1
    i = 0
    second = []
    while i < n-1:
        second.append(k)
        k += 2
        i += 1
        
    last = sum_first-sum(second)
    second.append(last)
    return second
t = int(input())

n_list = []
i = 0
while i<t:
    n_list.append(int(input()))
    i+=1
    
for n in n_list:
    if (n//2)%2 != 0:
        print('NO')
    else:
        print('Yes')
        first = make_first(n//2)
        second = make_second(n//2,sum(first))
        first.extend(second)
        ans = [str(a) for a in first]
        print(' '.join(ans))