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:
from bisect import bisect, bisect_left, bisect_right


def solve():
    n, k = map(int, input().split())
    ar = list(map(int, input().split()))

    ocr = {}
    mpv = [None] * (n // 2)
    spv = [None] * (n // 2)

    for i in range(n // 2):
        x = ar[i] + ar[n - i - 1]
        mpx = max(ar[i], ar[n - i - 1]) + k
        spx = min(ar[i], ar[n - i - 1]) + 1

        spv[i] = spx
        mpv[i] = mpx

        if x in ocr:
            ocr[x] += 1
        else:
            ocr[x] = 1

    mpv.sort()
    spv.sort()

    items = [(v, k) for k, v in ocr.items()]
    items.sort()
    items.reverse()

    best = n // 2

    for ocr, x in items:
        over = bisect_left(mpv, x, 0, len(mpv))
        under = n // 2 - bisect_right(spv, x, 0, len(spv))

        cur = n // 2 - ocr + over + under

        if cur < best:
            best = cur

    print(best)


t = int(input())

for _ in range(t):
    solve()

# solve()