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 collections import *
from bisect import *
#from math import *
import sys
input=sys.stdin.readline
t=int(input())
while(t):
    t-=1
    n,k=map(int,input().split())
    a=list(map(int,input().split()))
    r=[0 for i in range((2*k)+2)]
    for i in range(n//2):
        x=a[i]
        y=a[n-i-1]
        st=min(x,y)+1
        end=min(2*k,max(x,y)+k)
        #print(st,end)
        r[st]-=1
        if(end!=2*k):
            r[end+1]+=1
        if(st!=2):
            r[2]-=2
            r[st]+=2
        if(end!=2*k):
            r[end+1]-=2
    for i in range(1,(2*k)+2):
        r[i]+=r[i-1]
    for i in range(n//2):
        r[a[i]+a[n-i-1]]+=1
    x=max(r[2:-1])
    if(x>=0):
        print(0)
    else:
        print(abs(x))