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:
import sys
from array import array  # noqa: F401
import typing as Tp  # noqa: F401


def input():
    return sys.stdin.buffer.readline().decode('utf-8')


def main():
    t = int(input())
    ans = [''] * t

    for ti in range(t):
        n, k = map(int, input().split())
        a = list(map(int, input().split()))
        pair_cnt = n >> 1
        ub = k * 2 + 1
        cost1 = [0] * (ub + 1)
        cost2 = [0] * (ub + 1)
        cnt = [0] * (ub + 1)

        for i in range(n >> 1):
            x, y = a[i], a[-i - 1]
            if x > y:
                x, y = y, x
            cost1[k + y + 1] += 1
            cost2[x] += 1
            cnt[x + y] += 1

        for i in range(ub):
            cost1[i + 1] += cost1[i]
        for i in range(ub, 0, -1):
            cost2[i - 1] += cost2[i]

        mincost = 10**9

        for i in range(1, ub + 1):
            c = cost1[i] + cost2[i] + (pair_cnt - cnt[i])
            if mincost > c:
                mincost = c

        ans[ti] = str(mincost)

    sys.stdout.buffer.write(('\n'.join(ans) + '\n').encode('utf-8'))


if __name__ == '__main__':
    main()