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())
pole_neparne = [1]
pole_neparne_index = 1
pole_parne = [2]
pole_parne_index = 1
for x in range(t):
    n = int(input())
    if n % 4 !=0 or n == 0:
        print("NO")
    else:
        pocet = int(n/2)
        if pole_neparne_index < pocet+1:
            while pole_neparne_index <= pocet:
                pole_neparne.append(pole_neparne[-1]+2)
                pole_neparne_index += 1


        if pole_parne_index < pocet:
            while pole_parne_index <= pocet:
                pole_parne.append(pole_parne[-1]+2)
                pole_parne_index += 1

        print('YES')
        print(*pole_parne[0:pocet], sep=' ',end=' ')
        print(*pole_neparne[0:int(pocet/2)], sep=' ',end=' ')
        print(*pole_neparne[int(pocet/2+1):pocet+1], sep=' ')