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:
out=[]
for i in range(int(input())):
    n=int(input())
    even=[]
    odd=[]
    even_s=""
    odd_s=""
    for i in range(2,n+1):
        if i%2==0:
            even.append(i)
    sum_even=sum(even)
    if len(even)%2==0:
        for i in range(1,sum_even+1):
            if i%2!=0:
                odd.append(i)
                if len(odd)==len(even)-1:
                    odd.append(sum_even-sum(odd))
                    break
        for i in even:
            even_s+=str(i)+" "
        for i in odd:
            odd_s+=str(i)+" "
        out.append("YES")
        out.append(even_s+odd_s)
    else:
        out.append("NO")
for i in out:
    print(i,end="\n")