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 os
from collections import defaultdict


def f(nums, k):
    n = len(nums)
    n2 = n // 2
    p = defaultdict(int, {})
    mi = defaultdict(int, {})
    ma = defaultdict(int, {})
    for i in range(n2):
        p[nums[i] + nums[n - i - 1]] += 1
        mi[min(nums[i], nums[n - i - 1])] += 1
        ma[max(nums[i], nums[n - i - 1])] += 1


    mlx = 0
    mgx = 0
    cost = n
    for x in range(2 * k + 1):
        mlx += mi[x - 1]
        mgx += ma[x - k - 1]
        cost = min(n - mlx - p[x] + mgx, cost)

    return cost

#f(list(map(int, "6 1 1 7 6 3 4 6".split())), 7)

def pp(input):
    n_test = int(input())
    for i in range(n_test):
        k = int(input().split()[1])
        print(f(list(map(int, input().split())), k))


if "paalto" in os.getcwd():
    from string_source import string_source

    s = string_source(
        """4
4 2
1 2 1 2
4 3
1 2 2 1
8 7
6 1 1 7 6 3 4 6
6 6
5 2 6 1 3 4"""
    )

    pp(s)
else:
    pp(input)