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 math import *
from bisect import bisect_left, bisect_right
from queue import Queue
from sys import stdin, stdout
from collections import Counter
input = lambda: stdin.readline().strip()
fast_print = stdout.write
 
t = int(input())
for _ in range(t):
    n, k = map(int, input().split())
    ls = list(map(int, input().split()))
    check_min = []
    check_max = []
    sums = {}
    for i in range(n//2):
        check_min.append(min(ls[i], ls[n-i-1])+1)
        check_max.append(max(ls[i], ls[n-i-1])+k)
        try: sums[ls[i]+ls[n-i-1]]+=1
        except: sums[ls[i]+ls[n-i-1]] = 1
    check_min.sort()
    check_max.sort()
    ans = n-2
    for s in range(2, 2*k+1):
        fail1 = (n//2)-bisect_right(check_min, s)
        fail2 = bisect_left(check_max, s)
        cur_ans = (n//2)+fail1+fail2
        try: cur_ans-=sums[s]
        except: pass
        ans = min(ans, cur_ans)
    fast_print(str(ans)+'\n')