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:
respostas = []


testcase = int(input())

def lista(caso):
    primeira_metade = []
    segunda_metade = []
    par = 2
    impar = 1
    for ad in range(caso//2):
        primeira_metade.append(par)
        segunda_metade.append(impar)
        par += 2
        impar += 2
    if sum(primeira_metade) != sum(segunda_metade):
        x = sum(primeira_metade) - sum(segunda_metade)
        segunda_metade[-1] += x
    result = primeira_metade + segunda_metade
    return result

for each in range(testcase):
    n = int(input())
    if n % 4 != 0:
        respostas.append("NO")
    elif n % 4 == 0:
        result = lista(n)
        respostas.append("YES")
        crc = " ".join(str(num) for num in result)
        respostas.append(crc)

for resp in respostas:
    print(resp)