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 solve():
    T = int(input())
    for t in range(T):
        n = int(input()) # even
        #odd + odd = even
        #odd + even = odd
        #even + even = even

        if (n // 2) % 2 == 1:
            print('NO')
            continue        
        
        print('YES')

        arr = []
        even_acc = 0
        odd_acc = 0
        for i in range(2, n+1, 2):
            arr.append(i)
            even_acc += i
        for i in range(1, n+1, 2):
            arr.append(i)
            odd_acc += i
        while even_acc != odd_acc:
            arr[-1] = arr[-1] + 2
            odd_acc += 2
        for n in arr:
            print(n, end=' ')
        # 4 => [2,4], [1,5]
        # 8 => [2,4,6,8], [1,3,5,11]


#2 4 6 8 10 12 1 3 5 7 9 17
#print(sum([2, 4, 6, 8, 10, 12]))
#print(sum([1, 3, 5, 7, 9, 17]))
solve()