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())
while T > 0:
    T = T - 1
    N, K = map(int, input().split(" "))
    nums = list(map(int, input().split(" ")))
    sums = [0] * (2 * K + 1)
    prefs = [0] * (2 * K + 2)
    i = 0
    terms = int(N/2)
    while i < terms:
        curr_ind = i * 2
        curr = nums[curr_ind] + nums[N - curr_ind - 1]
        sums[curr] = sums[curr] + 1
        minim = 1 + min(nums[curr_ind], nums[N - curr_ind - 1])
        maxim = K + max(nums[curr_ind], nums[N - curr_ind - 1])
        prefs[minim] = prefs[minim] + 1
        prefs[maxim + 1] = prefs[maxim + 1] - 1
        i = i + 1

    i = 1
    while i < len(prefs):
        prefs[i] = prefs[i] + prefs[i - 1]
        i = i + 1

    i = 1
    cost = -1
    while i < len(sums):
        now_cost = sums[i] * 0 + (prefs[i] - sums[i]) + (terms - prefs[i]) * 2
        if cost == -1 or now_cost < cost:
            cost = now_cost
        i = i + 1
    print(cost)