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 sys import stdin

debug = False


def join(_s, _l):
    return _s.join(map(str, _l))


def read(_f=None):
    if _f == None:
        return stdin.readline().strip()
    return _f(stdin.readline().strip())


def readlist(_f=None):
    _l = stdin.readline().strip().split()
    if _f == None:
        return _l
    return map(_f, _l)


readint = lambda: read(int)
readints = lambda: readlist(int)
printval = lambda _r: print(_r, end=" ")
printline = lambda _s, _r: print(join(_s, _r), end="\n")


def solve():
    n = readint()
    nums = n // 2
    if nums % 2 == 0:
        first = [0] * nums
        second = [0] * nums
        number = 2
        for i in range(nums):
            first[i] = number
            if i % 2 == 0:
                second[i] = number - 1
            else:
                second[i] = number + 1
            number += 4

        return True, first + second
    else:
        return False, []


if __name__ == "__main__":
    t = readint()
    for _ in range(t):
        if debug:
            print("-" * 20)
        if debug:
            print("ANS: ", end="")

        possible, array = solve()

        if possible:
            print("YES")
            printline(" ", array)
        else:
            print("NO")