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:
# Problem: https://codeforces.com/problemset/problem/1343/B


def main(n):
    if n // 2 % 2 == 1:
        return "NO"
    else:
        valid = "YES\n"
        l_half, r_half = [], []
        l_sum, r_sum = 0, 0

        for i in range(2, n+1, 2):
            l_half.append(str(i))
            l_sum += i
        for j in range(1, n-2, 2):
            r_half.append(str(j))
            r_sum += j
        r_half.append(str(l_sum - r_sum))

        return valid + " ".join(l_half + r_half)

if __name__ == "__main__":
    # Take input
    t = int(input())
    cases = []
    for i in range(t):
        cases.append(int(input()))

    # Run main
    for case in cases:
        print(main(case))