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:
import math
t=int(input())
for i in range(t):
    n=int(input())
    if 1==1:
        ans=[]
        ans1=[]
        i1=3
        i2=2*n-1
        x1=2
        x2=2*n
        sum1=0
        sum2=0
        if n==2 or (n//2)%2 ==1:
            print("NO")
            continue
        
        while(len(ans)<n//2 and x1<x2 and i1<i2):
            ans.append(i1)
            ans.append(i2)
            sum1+=i1+i2
            i1+=2
            i2-=2
            ans1.append(x1)
            ans1.append(x2)
            sum2+=x1+x2
            x1+=2
            x2-=2
            if len(ans)==n//2:
                break
        c=ans1+ans
        if sum1==sum2:
            print("YES")
            print(*c)
        else:
            print("NO")