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:

for _ in range(int(input())):
    n=int(input())
    a=[]
    c=1
    x=2
    s1=0
    while c<=(n//2):
        a.append(x)
        s1+=x
        x+=2
        c+=1
    y=1
    s2,c=0,1
    while c<(n//2):
        a.append(y)
        c+=1 
        s2+=y
        y+=2 
    odd=y
    # print(a)
    # print(odd)
    flag=True
    while True:
        if odd+s2==s1:
            print("YES")
            print(' '.join(map(str,a))+" "+str(odd))
            break
        elif odd+s2>s1:
            flag=False
            break
        else:
            odd+=2
    if not flag:print("NO")