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 Counter
import bisect
n_cases = int(input())
for case_num in range(n_cases):
    n, k = [int(x) for x in input().split()]
    arr = [int(x) for x in input().split()]
    m = n // 2
    maxes = []
    mins = []
    ctr = Counter()
    for i in range(n// 2):
      x = arr[i]
      y = arr[n - i - 1]
      maxes.append(max(x, y) + k)
      mins.append(min(x, y) + 1)
      ctr[x + y] += 1
    maxes = sorted(maxes)
    mins = sorted(mins)
    # print('='*30)
    # print(arr)
    # print(maxes)
    # print(mins)
    # print('-'*30)
    best = 2**30
    for s in range(2, 2*k+1):
      cnt = ctr[s]
      n_max_bad = bisect.bisect_left(maxes, s)
      n_min_bad = m - bisect.bisect_right(mins, s)
      cost = m - cnt + n_max_bad + n_min_bad
      #print(f"s: {s} ; cnt: {cnt} ; nMb: {n_max_bad}; nmb: {n_min_bad}; cost: {cost}")
      best = min(best, cost)
    print(best)