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 Fri May 22 18:09:43 2020

@author: Admin
"""


test_case = int(input())

while test_case > 0:
     boo = False
     size = int(input())
     n = size // 2
     sum_even = n * (n + 1)
     sum_odd = (n-1)*(n-1)
     
     i = size - 1
     while sum_even >= sum_odd + i:
          if sum_odd + i == sum_even:
               boo = True
               break
          else:
               i += 2
               temp = i
     
     if boo :
          print("YES")
          for j in range(2 , size + 1 , 2):
               print(j , end = " ")
          for j in range(1 , size - 2 , 2):
               print(j , end = " ")
          print(temp)
          
     else:
          print("NO")
          
     test_case -= 1