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 foo(n, data, k):
    farr = [0] * (2 * k + 1)
    sarr = [0] * (2 * k + 2)
    i = 0
    while i < n // 2:
        farr[data[i] + data[size - i - 1]] += 1
        i += 1
    i = 0
    while i < n // 2:
        sarr[min(data[i], data[size - i - 1]) + 1] += 1
        sarr[max(data[i], data[size - i - 1]) + k + 1] -= 1
        i += 1
    i = 1
    while i < (2 * k + 1):
        sarr[i] += sarr[i - 1]
        i += 1
    i = 0
    minimum = int(2 * 10e5)
    while i <= k * 2:
        minimum = min(minimum, (sarr[i] - farr[i]) + 2 * (n // 2 - sarr[i]))
        i += 1

    print(minimum)

if __name__ == '__main__':
    test = int(input())
    while test:
        size, k = [int(x) for x in input().split()]
        data = [int(i) for i in input().split()]
        foo(size, data, k)
        test -= 1