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())

ans1=[0]*t
ans2=[0]*t


for j in range(t):
    n=int(input())

    if (n%4==2):
        ans1[j]=0
    else:
        ans1[j]=1

        ans2[j]=[0]*n

        for i in range (1,n//2):
            ans2[j][i-1]=i*2

        ans2[j][n//2-1]=n//2*2


        for i in range(1,(n//2)):
            ans2[j][i+(n//2)-1]=i*2-1
        ans2[j][n-1]=n + n//2 -1 

for i in range(t):
    if (ans1[i]==0):
        print("NO")
    else:
        print("YES")

        for j in range(len(ans2[i])):
            print (ans2[i][j], end=" ")
        print()