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:
from bisect import bisect_right,bisect_left
a=int(input())
for i in range(a):
    n,k=map(int,input().split())
    z=list(map(int,input().split()))
    
    from collections import defaultdict
    al=defaultdict(int)
    mini=[]
    maxa=[]
    for i in range(len(z)//2):
        al[z[i]+z[n-i-1]]+=1
        mini.append(1+min(z[i],z[n-i-1]))
        maxa.append(k+max(z[i],z[n-i-1]))
    count=0
    for i in range(len(z)//2):
        if(z[i]+z[n-i-1]==k+1):
            continue;
        if(mini[i]<=k+1<=maxa[i]):
            count+=1
        else:
            count+=2
    ans=count
    mini.sort()
    maxa.sort()
    for i in range(1,(2*k)+1):
        if(i<k+1):
            t=bisect_right(mini,i)
            ans=min(ans,t+(len(mini)-t)*2-al[i])
        elif(i>k+1):
            t=bisect_left(maxa,i)
            ans=min(ans,(len(maxa)-t)+2*t-al[i])
    print(ans)
        
    
    
    
    
mini=[]
maxa=[]