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:
t = int(input())

for i in range(t):
    n, k = map(int, input().split())
    a = list(map(int, input().split()))

    sum_costs = [n // 2] * (k * 2 + 1)
    lower_penalties = [0] * (k * 2 + 1)
    upper_penalties = [0] * (k * 2 + 1)
    for ai, aj in zip(a[:n // 2], reversed(a[n // 2:])):
        sum_costs[ai + aj] -= 1
        lower_penalties[min(ai, aj)] += 1
        if max(ai, aj) < k:
            upper_penalties[max(ai, aj) + k + 1] += 1
    for j in range(k * 2 - 1, -1, -1):
        lower_penalties[j] += lower_penalties[j + 1]
    for j in range(1, k * 2 + 1):
        upper_penalties[j] += upper_penalties[j - 1]
    for j in range(k * 2 + 1):
        sum_costs[j] += lower_penalties[j] + upper_penalties[j]
    print(min(sum_costs[2:]))