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())


def solve(N):
    out_li = [0 for x in range(N)]
    num = 2
    for i in range(N//2):
        out_li[i] = num
        num += 2

    check_odd = out_li[N//2-1]+(N//2-1)
    if check_odd % 2 == 0:
        return False
    num = 1
    for i in range(N//2, N-1):
        out_li[i] = num
        num += 2
    out_li[-1] = check_odd
    return out_li


ans = []
for _ in range(T):
    N = int(input())
    if solve(N) == False:
        ans.append("NO")
    else:
        ans.append("YES")
        ans.append(solve(N))

for item in ans:
    if type(item) == str:
        print(item)
    else:
        for num in item:
            print(num, end=' ')
        print()