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:
from sys import stdin
input=stdin.readline

def A():
    li=[]
    for i in range(2, 30):
        li.append(2**i - 1)
    for _ in range(int(input())):
        n=int(input())
        j=0
        while j<len(li):
            if n % li[j] == 0:
                print(n//li[j])
                break
            j += 1
    return

def B():
    for _ in range(int(input())):
        n=int(input())
        if n//2 % 2 == 1: print("NO")
        else:
            print("YES")
            arr=[0]*n
            for i in range(1,n//2+1): arr[i-1]=2*i
            for i in range(n//2, n-1): arr[i]=2*(i-n//2)+1
            arr[n-1] = sum(arr[:n//2])-sum(arr[n//2:])
            print(*arr)
    return

def C():
    return

def D():
    return

def E():
    return

B()