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:
T = int(input())


def main():
  n = int(input())
  
  if n%4==2:
    return("NO")
  else:
    a = []
    for k in range(1, int(n/2)+1):
      a.append(str(k))
    
    a = a + a
    a[int(n/2)-1] = str(int(a[int(n/2)-1]) + int(n/4))


    for k in range(0, int(n/2)):
      a[k] = str(int(a[k])*2)
      a[k+int(n/2)] = str(int(a[k+int(n/2)])*2 + 1)

    myString = " ".join(a)
    return("YES \n" + myString)
  
#print(" ".join(my_list))
#8 
#k1 + k2 + k3 + k4 = q1 + q2 + q3 + q4 + 2

for _ in range(T):
  print(main())