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:
n = int(input())

tests = [int(input()) for _ in range(n)]

answers = []
for test in tests:
    test = test // 2
    if test % 2 != 0:
        answers.append('NO')
    else:
        temp1 = [2]
        temp2 = [1]
        for _ in range(test-1):
            temp1.append(temp1[-1]+2)
        stemp1 = sum(temp1)
        for _ in range(test-2):
            temp2.append(temp2[-1]+2)
        stemp2 = sum(temp2)
        temp2.append(stemp1 - stemp2)
        answers.append('YES')
        answers.append(temp1+temp2)

for _ in answers:
    if type(_) == list:
        [print(i, end=' ') for i in _]
        print('')
    else:
        print(_)