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
# sys.setrecursionlimit(10**6)
input = sys.stdin.buffer.readline
# arr = [[int(el) for el in input().split()] for i in range(n)]


def solve(n):

    if (n // 2)&1:
        return []

    arr = [0] * n

    even = 0
    odd = n // 2
    for i in range(1, n + 1):
        if i&1:
            arr[odd] = i
            odd += 1
        else:
            arr[even] = i
            even += 1

    arr[-1] += n // 2

    return arr


t = int( input() )

for _ in range(t):

    n = int(input())

    ans = solve(n)

    if not ans:
        print ('NO')

    else:
        print ('YES')

        fans = ' '.join(map(str, ans))

        print (fans)