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 convert(n):
    s = [str(d) for d in n]
    res = (" ".join(s))
    return (res)


t = int(input())
i = 0
v = []
for i in range(t):
    n = int(input())
    v.append(n)
for d in v:
    k = []
    g = 0
    p = 0
    l = 2
    m = 1
    for s in range(d+1):
        if d == 2 + 4*g:
            k.clear()
            break
        elif s < d//2:
            k.append(l)
            p += l
            l = l + 2

        elif s>d//2 and s<d:
            k.append(m)
            p -= m
            m = m + 2

        elif s == d:
            k.append(p)
        g += 1

    if k == []:
        print("No")
    else:
        print("Yes")
        print(convert(k))