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:
#*****DO NOT COPY*****
#F
#U       ___                     ___                         ___           ___           ___           ___          _____
#C      /  /\      ___          /  /\          ___          /__/\         /  /\         /  /\         /  /\        /  /::\
#K     /  /::\    /  /\        /  /:/_        /  /\         \  \:\       /  /::\       /  /::\       /  /:/_      /  /:/\:\
#     /  /:/\:\  /  /:/       /  /:/ /\      /  /::\         \  \:\     /  /:/\:\     /  /:/\:\     /  /:/ /\    /  /:/  \:\
#Y   /  /:/~/:/ /__/::\      /  /:/ /::\    /  /:/\:\    ___  \  \:\   /  /:/~/::\   /  /:/~/:/    /  /:/ /:/_  /__/:/ \__\:|
#O  /__/:/ /:/  \__\/\:\__  /__/:/ /:/\:\  /  /:/~/::\  /__/\  \__\:\ /__/:/ /:/\:\ /__/:/ /:/___ /__/:/ /:/ /\ \  \:\ /  /:/
#U  \  \:\/:/      \  \:\/\ \  \:\/:/~/:/ /__/:/ /:/\:\ \  \:\ /  /:/ \  \:\/:/__\/ \  \:\/:::::/ \  \:\/:/ /:/  \  \:\  /:/
#    \  \::/        \__\::/  \  \::/ /:/  \  \:\/:/__\/  \  \:\  /:/   \  \::/       \  \::/~~~~   \  \::/ /:/    \  \:\/:/
#A    \  \:\        /__/:/    \__\/ /:/    \  \::/        \  \:\/:/     \  \:\        \  \:\        \  \:\/:/      \  \::/
#L     \  \:\       \__\/       /__/:/      \__\/          \  \::/       \  \:\        \  \:\        \  \::/        \__\/
#L      \__\/                   \__\/                       \__\/         \__\/         \__\/         \__\/
#
#
#*****DO NOT COPY*****

for i in range(int(input())):

    n = int(input())
    out = []

    if (n/2) % 2 == 1:
        print('NO')

    else:
        print("YES")
        for i in range(1 , int((n/2) + 1)):
            out.append(2 * i)

        for i in range(int(n/2)):
            if i < n/4:
                out.append(out[i] - 1)
            else:
                out.append(out[i] + 1)

        for i in range(len(out)):
            print(out[i] , end = " ")
        print()