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:
'''test=int(input())
for i in range(test):
    n=int(input())
    a=[int(j) for j in input().split()]
    b=[int(k) for k in input().split()]
    ans=""
    if a[0]!=b[0]:
        ans="NO"
    else:
        pos=0
        neg=0
        for i in range(n):
            if a[i]>b[i] and  not neg:
                ans="NO"
                break

            elif a[i]<b[i] and not pos:
                ans="NO"
                break
            else:
                if a[i]==1:
                    pos+=1
                elif a[i]==-1:
                    neg+=1
                ans="YES"
    print(ans)'''

'''n=int(input())
nums=[int(i) for i in input().split()]
from collections import defaultdict
hashmap=defaultdict(int)
sum_=0
ans=0
for i in range(n):
    sum_+=nums[i]
    if sum_ in hashmap:
        ans+=(n-i)*hashmap[sum_]
        hashmap[sum_]+=1
    elif sum_ not in hashmap and not sum_:
        ans+=n-i
        hashmap[0]+=1
    else:
        hashmap[sum_]+=1
print(int(n*(n+1)/2-ans))'''

'''import heapq
test=int(input())
for i in range(test):
    n=int(input())
    monst=[]
    kill=[0]*n
    for j in range(n):
        a,b=[int(i) for i in input().split()]
        monst.append((a,b,j))
    heap=sorted(monst,key=lambda x:x[0]-x[1])
    penalty=[0]*n
    bull=0
    for k in range(n):
        if not kill[heap[k][2]]:
            bull+=heap[k][0]
            start=k
            next_=0 if k==n-1 else k+1
            while monst[]

'''
'''test=int(input())
for i in range(test):
    a,b,c,d=[int(i) for i in input().split()]
    first=b
    second=c
    third=c
    
    print(first,second,third,sep=" ")'''

'''
test=int(input())
for i in range(test):
    x,n,m=[int(i) for i in input().split()]
    ans="NO"
    if n==m==0:
        ans="NO"
    else:
        spell1=0
        spell2=0
        for i in range(n):
            if x<=0 or x<=m*10:
                ans="YES"

            x=int(x/2)+10

        if x<=0 or x<=m*10:
            ans="YES"



    print(ans)
    '''

'''n,k=[int(i) for i in input().split()]
from collections import defaultdict
graph=defaultdict(list)
for i in range(n-1):
    p,c=[int(i) for i in input().split()]
    graph[p].append(c)
    graph[c].append(p)

size=[0]*(n+1)
depth=[0]*(n+1)
depth[0]=-1
ans=[0]*(n+1)
def dfs(p,c):
    size[c]=1
    depth[c]=1+depth[p]
    for j in graph[c]:
       if j!=p:
            size[c]+=dfs(c,j)
    ans[c]=size[c]-depth[c]
    return size[c]    
            
    

dfs(0,1)

ans.sort(reverse=True)
res=sum([ans[a] for a in range(n-k)])
print(res)

print(ans)
'''


test=int(input())
for i in range(test):
    n=int(input())
    ans=[]
    str="NO"
    t=int(n/2)
    if (t*(t+1)-(t-1)**2)%2==0:
        print(str)
    else:
        str="YES"
        for j in range(int(n/2)):
            ans.append((j+1)*2)
        for k in range(int(n/2)-1):
            ans.append(2*k+1)
        ans.append(t*(t+1)-(t-1)**2)
        print(str)
        for i in ans:
            print(i,end=" ")