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 PYTHON):

Solution:
import sys

__author__ = 'ratmir'

[t] = [int(x) for x in sys.stdin.readline().split()]


def getN(n):
    if n % 4 != 0:
        return "NO"
    ln = n / 2
    sm = ln * (ln + 1) / 2
    mnl = 2 * sm
    mnr = 2 * sm - ln
    # print mnl, mnr
    output = "YES\n"
    sm = 0
    results = []
    for i in range(0, n / 2):
        i_ = 2 * (i + 1)
        sm += i_
        results.append(i_)
    sm2 = 0
    for i in range(0, (n / 2) - 1):
        i_ = 2 * i + 1
        sm2 += i_
        results.append(i_)
    results.append(sm - sm2)
    output += (''.join('{} '.format(k) for k in results))
    return output


for ti in range(0, t):
    [n] = [int(x1) for x1 in sys.stdin.readline().split()]
    # n = n + 1

    print getN(n)