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
input=sys.stdin.readline
def bs(l,target,n):
    low=0
    high=n
    ans=-1
    while low<=high:
        mid=low+(high-low)//2
        if l[mid]<=target:
            ans=max(ans,mid)
            low=mid+1
        else:
            high=mid-1
    return ans
t=int(input())
for r in range(t):
    n,k=map(int,input().split())
    l=list(map(int,input().split()))
    d={}
    start=[]
    end=[]
    i=0
    j=n-1
    while i<j:
        start.append(min(l[i],l[j])+1)
        end.append(max(l[i],l[j])+k)
        try:
            d[l[i]+l[j]]+=1
        except:
            d[l[i]+l[j]]=1
        i+=1
        j-=1


    start.sort()
    end.sort()
    mini=999999999999999
    for i in range(1,(2*k)+1):
        a=bs(start,i,len(start)-1)+1
        b=bs(end,i-1,len(end)-1)+1
        # print(a,b)
        one=a-b
        zero=0
        try:
            zero=d[i]
        except:
            pass
        twos=(n//2)-(one)
        ans=(twos*2)+(one-zero)
        # print("x: "+str(i)+" ans: "+str(ans))
        # print("0: "+str(zero)+" 1: "+str(one-zero)+" 2: "+str(twos))
        mini=min(mini,ans)
    print(mini)