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 collections


def solve(n):
    if n % 4 != 0:
        print("NO")
        return

    evens = []
    odds = []

    # currFirstEven = 2
    # odd = 1

    # for i in range(0, n, 4):
    #     totalEvenSum = currFirstEven + currFirstEven + 2
    #     evens.append(currFirstEven)
    #     evens.append(currFirstEven + 2)

    #     odds.append(totalEvenSum-odd)
    #     odds.append(totalEvenSum - odds[-1])

    #     currFirstEven += 4
    #     odd += 2

    # return evens + odds

    evenSum = 0
    oddSum = 0

    for even in range(2, n+1, 2):
        evens.append(even)
        evenSum += even

    for odd in range(1, n-1, 2):
        odds.append(odd)
        oddSum += odd

    odds.append(evenSum - oddSum)

    print("YES")
    print(" ".join(map(str, evens + odds)))


t = int(input().strip())
# [n,m] = list(map(int, input().strip().split()))

for i in range(t):
    n = int(input().strip())

    solve(n)