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

t = int(input())
for _ in range(t):
    n, m = map(int, input().split())
    ip = [int(k) for k in input().split()]
    li = [[] for i in range(n // 2)]
    n = len(ip)
    for j in range(n // 2):
        li[j].append(min(ip[j], ip[n - j - 1]))
        li[j].append(max(ip[j], ip[n - j - 1]))
    ans = 10 ** 10

    prefix = [0] * ((2*m)+5)
    hash0=defaultdict(int)
    for j in range(n // 2):

        hash0[ip[j] + ip[n - j - 1]] += 1
        prefix[li[j][0] + 1] += 1
        prefix[li[j][1] + m + 1] -= 1
        tot = 0
    for i in range(0, 2 * m + 1):
        tot += prefix[i]
        prefix[i] = tot
        # mina=100000000
    for i in range(2, 2 * m + 1):
        c0 = hash0[i]
        c1 = prefix[i] - c0
        c2 = n // 2 - (c0 + c1)
        ans = min(ans, 2 * c2 + c1)
    print(ans)