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:
x=0
y=1
ans = 0
ans2 = 0
n = int(input())
arr = list()
for i in range(0 , n):
    a = int(input())
    for k in range(0 , a//2):
        x += 2
        arr.append(x)
    for k in range(0 , a//2):
        if k == a//2-1:
            var = sum(arr[0:a//2]) - sum(arr[a//2:a-1])
            if var%2==0:
                var+=1
            arr.append(var)
        else:
            arr.append(y)
            y+=2
    if sum(arr[0:a//2]) == sum(arr[a//2:a]):
        print('YES')
        for k in arr:
            print(k , end = ' ')
        print('\n')
    else:
        print('NO')

    arr.clear()    
    ans2 = 0
    ans = 0
    x = 0
    y=1