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:
import sys
import math
from collections import defaultdict
def lower(arr,num):
    if num>arr[-1]:
        return len(arr)
    l,r=0,len(arr)-1
    ans=-1
    while l<=r:
        mid=(l+r)//2
        if arr[mid]<num:
            l=mid+1
            ans=mid
        else:
            r=mid-1
    return ans
def lowera(arr,num):
    if num>arr[-1]:
        return len(arr)-1
    l,r=0,len(arr)-1
    ans=-1
    while l<=r:
        mid=(l+r)//2
        if arr[mid]<=num:
            l=mid+1
            ans=mid
        else:
            r=mid-1
    return ans
t=int(sys.stdin.readline())
for _ in range(t):
    dic=defaultdict(int)
    n,k=map(int,sys.stdin.readline().split())
    arr=list(map(int,sys.stdin.readline().split()))
    small=[]
    large=[]
    l,r=0,n-1
    while l<=r:
        dic[arr[l]+arr[r]]+=1
        small.append(min(arr[l],arr[r]))
        large.append(max(arr[l],arr[r]))
        l+=1
        r-=1
    small.sort()
    large.sort()
    for i in range(len(small)):
        small[i]+=1
    for i in range(len(large)):
        large[i]+=k
    small=[small[0]-1]+small
    large=[large[0]-1]+large
    #print(small,'small')
    #print(large,'large')
    #print(dic,'dic')
    ans=1e10
    for i in range(2,2*k+1):
        #print(i,'i')
        a=lowera(small,i)
        b=lower(large,i)
        #print(a,'a',b,'b')
        #a-=1
        x=n//2-a
        if b<1:
            y=0
            b=0
        #print(x,'x',y,'y')
        s=x*2+a+y*2+b-dic[i]
        #print(s,'s')
        ans=min(ans,s)
    print(ans)