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:
# coup_de_grace

from sys import stdin
from functools import lru_cache, cmp_to_key
from itertools import accumulate, product, permutations, combinations, combinations_with_replacement
from collections import Counter, deque
from bisect import bisect_left, bisect_right

def solver():

    line = stdin.readline()
    [n, k] = [*map(int, line.split())]
    line = stdin.readline()
    nums = [*map(int, line.split())]
    mn, mx, sum = [], [], []
    for i in range(n//2):
        mn.append(min(nums[i], nums[n-1-i]))
        mx.append(max(nums[i], nums[n-1-i]))
        sum.append(nums[i] + nums[n-1-i])
    mn.sort()
    mx.sort()
    cnt = [n // 2] * (2 * k + 1)
    for i in range(k + 1):
        pos = bisect_left(mn, i)
        cnt[i] += n // 2 - pos
    for i in range(k + 1, k * 2 + 1):
        pos = bisect_left(mx, i - k)
        cnt[i] += pos
    for i in sum:
        cnt[i] -= 1
    res = min(cnt)

    print('{}'.format(res))


def main():
    T = int(stdin.readline())
    for case_num in range(T):
        solver()


if __name__ == '__main__':
    main()