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:
#alpha = [ chr(i) for i in range(ord('a'),ord('z')+1)]
arr  = [[],[]]
def out1(x,n,m):
    # print(n,m)
    # if arr[n][m] != True:
    #     return False
    if x <= 0:

        return True
    if n <= 0 :
        if (x-10*m) > 0 :
            # arr[n][m] = False
            return False
        else:
            return True
    if m<=0 :
        # arr[n][m] = False
        return False
    # if n < 1:
    #     return out1(x-10,n,m-1)
    # elif m <= 0:

        
    return out1(x//2+10,n-1,m) or out1(x-10,n,m-1)



def out(x):
    if x%4!=0:
        print("NO")
        return
    print("YES")
    li = [i for i in range(1,x+2) if i!=x/2+1]
    for i in li:
        if i%2==0:
            print(i,end=" ")
    for i in li:
        if i%2!=0:
            print(i,end=" ")
        
    print()


for i in range(int(input())):
    x= int(input())
    out(x)