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 bisect import bisect_left as bl
from bisect import bisect_right as br
from heapq import heappush,heappop
import math
from collections import *
from functools import reduce,cmp_to_key
# import io, os
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
import sys
input = sys.stdin.readline

M = mod = 998244353
def factors(n):return sorted(set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))
def inv_mod(n):return pow(n, mod - 2, mod)

def li():return [int(i) for i in input().split()]
def st():return input()
def val():return int(input().rstrip('\n'))
def li2():return [i for i in input()]
def li3():return [int(i) for i in input()]


for _ in range(val()):
    n,k = li()
    l = li()
    cnt = Counter()
    mins = []
    maxs = []
    sums = []
    arr = [0]*(2*k + 5)
    for i in range(n//2):
        cnt[l[i] + l[n-i-1]] += 1
        a,b = max(l[i],l[n-i-1]),min(l[i],l[n-i-1])


        arr[b] += 1
        arr[a + k] -= 1


        maxs.append(a + k - b)
        mins.append(b + 1)

    mins.sort()
    maxs.sort()

    ans = n
    curr = arr[1]
    for i in range(2,2*k + 1,1):
        onecost = curr - cnt[i]
        twocost =  n//2 - curr
        ans = min(ans,onecost + twocost*2)
        curr += arr[i]
    print(ans)