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:
def solve(n):
    if n % 4 != 0:
        return "NO"
    ans = []
    e = 2
    o = 1
    half = n//2
    for i in range(half):
        ans.append(e)
        if i % 2 == 0:
            e += 2
        else:
            e += 4        
    for j in range(half):
        ans.append(o)
        if j % 2 == 0:
            o += 4
        else:
            o += 2
    return ("YES",ans)

  
def main():
    t = int(input())
    for i in range(t):
        n = int(input())
        # d = input()
        # d = [int(i) for i in d.split()]
        # a = d[0]
        # b = d[1]
        # c = d[2]
        ans = solve(n) 
        if ans == "NO":
            print(ans)       
        else:
            print(ans[0]) 
            l = ans[1]
            for k in l:    
                print(k ,end = " ")
            print()
main()