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 PYTHON):

Solution:
# coding=utf-8
# Author: lee215
# Date: 2020-04-23 00:00

get = lambda: int(raw_input().strip())
getl = lambda: raw_input().strip()
gets = lambda: map(int, raw_input().strip().split())
getss = lambda n: [gets() for _ in xrange(n)]

import collections

def solve(n, k, A):
    AI = sorted([A[i], i] for i in xrange(n))
    window = set()
    count = collections.Counter()
    left = right = 0
    max_save = save = 0
    # print 'AI', AI
    for S in xrange(2, k * 2 + 1):
        while right < n and AI[right][0] < S:
            a, i = AI[right]
            if n - 1 - i not in window:
                save += 1
            else:
                count[A[i] + A[n - 1 - i]] += 1
            window.add(i)
            right += 1

        while left < n and AI[left][0] < S - k:
            a, i = AI[left]
            if n - 1 - i not in window:
                save -= 1
            else:
                count[A[i] + A[n - 1 - i]] += 1
            window.remove(i)
            left += 1
        max_save = max(max_save, save + count[S])
        # print window, save, count
    return n - max_save

T = get()
for _ in xrange(T):
    n, k = gets()
    A = gets()
    res = solve(n, k, A)
    print res