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())
for _ in range(t):
    n=int(input())
    if n%4!=0:
        print("NO")
    else:
        l=[0]*n
        k=2
        for i in range(0,int(n/2)):
            l[i]=k
            k+=2
        #print('l=',l)
        fh=[2]
        sh=[1]
        lf=2
        ls=1
        sf=2
        ss=1
        for i in range(1,int(n/2)):
            if sf>ss:
                fh+=[lf+2]
                sf+=lf+2
                lf+=2
                sh+=[ls+4]
                ss+=ls+4
                ls+=4
            else:
                sh+=[ls+2]
                ss+=ls+2
                ls+=2
                fh+=[lf+4]
                sf+=lf+4
                lf+=4
        l=fh+sh
        print("YES")
        for i in range(len(l)):
            print(l[i],end=' ')
        print()