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 defaultdict as dc
from heapq import *
import math
import bisect
import sys
from collections import deque as dq
from heapq import heapify,heappush,heappop
mod=10**12
def inp(): 
    p=int(input())
    return p
def line():
    p=list(map(int,input().split()))
    return p
def read_mat():
    n=inp()
    a=[]
    for i in range(n):
        a.append(line())
    return a
def digit(n):
    s=str(n)
    p=0
    for i in s:
        p+=(int(i))**2
    return p
    
def check(a,b):
    for i in range(26):
        for j in range(len(a)+1):
            q=a[:j]+chr(97+i)+a[j:]
            if q==b:
                return 1
    return 0
def solve(a,n,k):
    p=dc(int)
    l=[]
    r=[]
    for i in range(n//2):
        p[a[i]+a[n-1-i]]+=1
    q=[0]*(2*k+2)
    for i in range(n//2):
        l,r=min(a[i],a[n-1-i]),max(a[i],a[n-1-i])
        q[l+1]+=1
        q[r+k+1]+=(-1)
    for i in range(1,len(q)):
        q[i]=q[i]+q[i-1]
    ans=float('inf')
    for i in range(2,2*k+1):
        ans=min(ans,(q[i]-p[i])+2*(n//2 - q[i]))
    return ans
for _ in range(inp()):
    n,k=line()
    a=line()
    l=solve(a,n,k)
    print(l)
    # print("Case #"+str(_+1)+":",l)