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())
n = [int(input()) for i in range(t)]
for a in n:
    if (a/2)%2==0 and (a/2)>1:
        print("YES")
        l = []
        for i in range(2,a+1,2):
            l.append(i)
        for i in range(1,a-1,2):
            l.append(i)
        l.append((a-1)+(a//2))
        print(*l)

    else:
        print("NO")


"""t = int(input())
for _ in range(t):
    n = int(input())
    if (n / 2) % 2 == 0:
        print('YES')
        print(' '.join([str(i) for i in range(2, n + 1, 2)] + [str(i) for i in range(1, n - 1, 2)] + [str((n - 1) + n // 2)]))
    else:
        print('NO')






t = int(input())

for _ in range(0, t):
    m = int(input())
    if m % 4 != 0:
        print("NO")
    else:
        print("YES")
        a = []
        for i in range(1, int(m / 2 + 1)):
            a.append(2 * i)
        for i in range(1, int(m / 4 + 1)):
            a.append(2 * i - 1)
        for i in range(int(m / 4 + 1), int(m / 2 + 1)):
            a.append(2 * i + 1)
        print(*a)"""