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:
w=int(input())
a=[]
if w>=1 and w<=10000:
    for i in range (0,w):
        p= int(input())
        if int(p)>=2 and int(p)<=200000:
            a.append(p)

    for i in range (0,w):
        b=[]
        c=[]
        sum1=0
        sum2=0
        r=a[i]
        if int(r)%4 != 0 :
            print("NO")
        else:
            print("YES")
            for t in range (2,int(r)+2,2):
                b.append(t)
                sum1=sum1+t
            for t in range (1,int(r)-2,2):
                c.append(t)
                sum2=sum2+t
            d=sum1-sum2
            c.append(d)
            b.extend(c)
            print(*b)