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:
t = int(input())

while t != 0:
    n = int(input())
    even_arr = list()
    odd_arr = list()

    initial_even_value = 0
    initial_odd_value = -1

    for i in range(n//2):
        initial_even_value += 2
        even_arr.append(initial_even_value)
    
    for i in range(n//2-1):
        initial_odd_value += 2
        odd_arr.append(initial_odd_value)

    if((sum(even_arr) - sum(odd_arr)) % 2 == 1):
        odd_arr.append(sum(even_arr) - sum(odd_arr))
    else:
        odd_arr.append(even_arr[-1] + 1)

    if(sum(even_arr) ==  sum(odd_arr)):
        print("YES")
        for i in even_arr:
            print(i, end=' ')
        for i in range(0,len(odd_arr)-1):
            print(odd_arr[i], end=' ')
        print(odd_arr[-1])
    else:
        print("NO")
    
    del(even_arr)
    del(odd_arr)

    t -= 1