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:
# -*- coding: utf-8 -*-
"""
Created on Thu May 14 13:00:10 2020

@author: Maarten
"""


def solve(n):
    answer = []
    if n%4 != 0:
        print('NO')
    else:
        print('YES')
        for i in range(1, n//2+1):
            answer.append(2*i)
        for i in range(1, n//2+1):
            answer.append(2*i-1)
        answer[n-1] += n//2
        print(' '.join(map(str, answer)))   # for int arrays
    
    return


if __name__ == '__main__':
    # fptr = open(os.environ['OUTPUT_PATH'], 'w')
    # fptr = open('01.txt')

    # t = int(fptr.readline().strip())
    t = int(input().strip())
    
    for _ in range(t):
        n = int(input().strip())
        # n.append(int(fptr.readline().strip()))
        result = solve(n)
        
    
    # print('\n'.join(result))          # for strings
    # print(' '.join(map(str, result)))   # for int arrays
    # print('\n'.join(map(str, result)))   # for int arrays
    # print('\n')