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:
def ans(n):
    mid = n//2
    if mid%2 is not 0:
        return 'NO', None
    
    arr = [0]*n
    l = 0
    even = 2
    while l < mid:
        arr[l] = even
        even +=2
        l+=1
    even_count = sum(arr)
    odd_count = 0
    odd = 1
    while l < n-1:
        arr[l] = odd
        odd_count += arr[l]
        l+=1
        odd +=2
    
    arr[l] = even_count - odd_count
    return 'YES', arr



t = int(input())
for i in range(t):
    x = int(input())
    a, b = ans(x)
    if b is None:
        print(a)
    
    else:
        print(a)
        for i in range(len(b)-1):
            print(b[i], end = ' ')
        
        print(b[len(b)-1])