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
#
# name = "input2.txt"
#
# sys.stdin = open( name )



def process(n):
    n1 = n//2
    if n1 % 2 != 0 :
        print('NO')
        return
    print('YES')
    list1 = [2 * i for i in range(1, n1 + 1)]

    list2 = [2 * i - 1 for i in range(1, n1)]
    last = sum(list1) - sum(list2)
    list2.append(last)
    r = ''
    first = True
    for a in list1:
        if first:
            r += str(a)
            first = False
        else:
            r += ' ' + str(a)
    for a in list2:
        r += ' ' + str(a)
    print(r)



input = sys.stdin.readline


def inp():
    return (int(input()))


def inlt():
    return (list(map(int, input().split())))


def insr():
    s = input()
    return (list(s[:len(s) - 1]))


def invr():
    return (map(int, input().split()))


def f(a, n):
    return True


def is_permutation(arr):
    for e in range(1, len(arr) + 1):
        if e not in arr:
            return False
    return True


t = inp()
for i in range(t):
    n = inp()
    process(n)